WorldCat Identities

Trotignon, Nicolas (1971-....).

Overview
Works: 19 works in 22 publications in 2 languages and 28 library holdings
Roles: Other, Opponent, Thesis advisor, Author, dgs
Publication Timeline
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Most widely held works by Nicolas Trotignon
Graphes parfaits : structure et algorithmes by Nicolas Trotignon( Book )

3 editions published between 2004 and 2005 in French and held by 3 WorldCat member libraries worldwide

Coloration, ensemble indépendant et structure de graphe by Lucas Pastor( )

1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide

This thesis deals with graph coloring, list-coloring, maximum weightstable set (shortened as MWSS) and structural graph theory.First, we provide polynomial-time algorithms for the 4-coloring problem insubclasses of P6-free graphs. These algorithms rely on a preciseunderstanding of the structure of these classes of graphs for which we give afull description.Secondly, we study the list-coloring conjecture and prove that for anyclaw-free perfect graph with clique number bounded by 4, the chromatic numberand the choice number are equal. This result is obtained by using adecomposition theorem for claw-free perfect graphs, a structural description ofthe basic graphs of this decomposition and by using Galvin's famous theorem.Next by using the structural description given in the first chapter andstrengthening other aspects of this structure, we provide polynomial-timealgorithms for the MWSS problem in subclasses of P6-free and P7-freegraphs.In the last chapter of the manuscript, we disprove a conjecture of De Simoneand K"orner made in 1999 related to normal graphs. Our proof is probabilisticand is obtained by the use of random graphs
The Four-in-a-Tree Problem in Triangle-Free Graphs by Nicolas Derhy( )

1 edition published in 2009 in English and held by 2 WorldCat member libraries worldwide

Sur quelques invariants classiques et nouveaux des hypergraphes by Andrea Munaro( )

1 edition published in 2016 in English and held by 2 WorldCat member libraries worldwide

In this thesis, we consider several hypergraph parameters and study whether restrictions to subclasses of hypergraphs allow to obtain desirable combinatorial or algorithmic properties. Most of the parameters we consider are special instances of packings and transversals of hypergraphs.In the first part, we focus on line graphs of subcubic triangle-free graphs and show that any such graph G has an independent set of size at least 3|V(G)|/10, the bound being sharp. As an immediate consequence, we obtain a tight lower bound for the matching number of subcubic triangle-free graphs. Moreover, we prove several algorithmic results related to FEEDBACK VERTEX SET, HAMILTONIAN CYCLE and HAMILTONIAN PATH when restricted to line graphs of subcubic triangle-free graphs.Then we consider three hypergraphs having the Erdős-Pósa Property and we seek to determine the optimal bounding functions. First, we provide an optimal theta-bounding function for the class of subcubic graphs and we study CLIQUE COVER: answering a question by Cerioli et al., we show it admits a PTAS for planar graphs. Then we focus on Tuza's Conjecture and show that the constant 2 in the statement can be improved for graphs whose edges are contained in at most four triangles and graphs obtained by forbidding certain odd-wheels. Finally, we concentrate on Jones' Conjecture: we prove it in the case of claw-free graphs with maximum degree at most 4 and we make some observations in the case of subcubic graphs.Then we study the VC-dimension of certain set systems arising from graphs. In particular, we consider the set system on the vertex set of some graph which is induced by the family of its k-connected subgraphs. Generalizing results by Kranakis et al., we provide tight upper and lower bounds for the VC-dimension and we show that its computation is NP-complete, for each k > 0. Finally, we show that this problem (in the case k = 1) and the closely related CONNECTED DOMINATING SET are either NP-complete or polynomial-time solvable when restricted to classes of graphs obtained by forbidding a single induced subgraph.In the final part of the thesis, we consider the following meta-questions: When does a certain “hard” graph problem become “easy”?; Is there any “boundary” separating “easy” and “hard” instances? In order to answer these questions in the case of hereditary classes, Alekseev introduced the notion of a boundary class for an NP-hard problem and showed that a problem Pi is NP-hard for a finitely defined (hereditary) class X if and only if X contains a boundary class for Pi. We continue the search of boundary classes for the following problems: HAMILTONIAN CYCLE THROUGH SPECIFIED EDGE, HAMILTONIAN PATH, FEEDBACK VERTEX SET, CONNECTED DOMINATING SET and CONNECTED VERTEX COVER
Sociabilités en ligne, usages et réseaux by Raphaël Charbey( )

1 edition published in 2018 in French and held by 2 WorldCat member libraries worldwide

With the digital advent, it is now possible for researchers to collect important amounts of data and online social network platforms are surely part of it. Sociologists, among others, seized those new resources to investigate over interaction modalities between individuals as well as their impact on the structure of sociability. Following this lead, this thesis work aims at analyzing a large number of Facebook accounts, through data analysis and graph theory classical tools, and to bring methodological contributions. Two main factors encourage to study Facebook social activities. On one hand, the importance of time spent on this platform by many Internet users justifies by itself the sociologists interest. On the other, and contrarily to what we observe on other social network websites, ties between individuals are similar to the ones that appear offline. First, the thesis proposes to detangle the multiple meanings that are behind the fact of ”being on Facebook”. The uses of our surveyed are not compacted in fantasized normative practices but vary depending on how they appropriate the different composers of the platform tools. These uses, as we will see it, do not concern all the socioprofessional categories in the same way and they also influence how the respondents interact with their online friends. The manuscript also explores these interactions, as well as the lover role into the relational structure. Second part of the thesis builds a typology of these relational structures. They are said as egocentred, which means that they are taken from the perspective of the respondent. This typology of social networks is based on their graphlet counts, that are the number of times each type of subnetwork appear in them. This approach offers a meso perspective (between micro and macro), that is propitious to underline some new social phenomena. With a high pluri-disciplinary potential, the graphlet methodology is also discussed and explored itself
A Polynomial Turing-Kernel for Weighted Independent Set in Bull-Free Graphs by Stéphan Thomassé( )

1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide

Excluding slightly more than a cycle = Exclure un peu plus qu'un cycle by Pierre Aboulker( Book )

2 editions published in 2013 in English and held by 2 WorldCat member libraries worldwide

Cette thèse concerne la théorie structurelle des graphes. Elle contient un certain nombre de résultats, aussi bien algorithmiques que structurels, sur les graphes ne contenant pas certains graphes en tant que sous graphes ou sous-graphes induits. Les graphes exclus consistent en des variations autour des configurations de Truemper. Celles-ci peuvent être vues comme des généalisations du cycle
Stable Sets in ISK4,wheel}-Free Graphs by Martin Milanič( )

1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide

Subdivisions de digraphes by Ana Karolinna Maia de Oliveira( )

1 edition published in 2014 in English and held by 1 WorldCat member library worldwide

In this work, we consider the following problem: Given a directed graph D, does it contain a subdivision of a prescribed digraph F? We believe that there is a dichotomy between NP-complete and polynomial-time solvable instances of this problem. We present many examples of both cases. In particular, except for five instances, we are able to classify all the digraphs F of order 4.While all NP-hardness proofs are made by reduction from some version of the 2-linkage problem in digraphs, we use different algorithmic tools for proving polynomial-time solvability of certain instances, some of them involving relatively complicated algorithms. The techniques vary from easy brute force algorithms, algorithms based on maximum-flow calculations, handle decompositions of strongly connected digraphs, among others. Finally, we treat the very special case of F being the disjoint union of directed cycles. In particular, we show that the directed cycles of length at least 3 have the Erdos-Pósa Property: for every n, there exists an integer tn such that for every digraph D, either D contains n disjoint directed cycles of length at least 3, or there is a set T of tn vertices that meets every directed cycle of length at least 3. From this result, we deduce that if F is the disjoint union of directed cycles of length at most 3, then one can decide in polynomial time if a digraph contains a subdivision of F
Trigraphes de Berge apprivoisés by Théophile Trunck( )

1 edition published in 2014 in French and held by 1 WorldCat member library worldwide

L'objectif de cette thèse est de réussir à utiliser des décompositions de graphes afin de résoudre des problèmes algorithmiques sur les graphes. Notre objet d'étude principal est la classe des graphes de Berge apprivoisés. Les graphes de Berge sont les graphes ne possédant ni cycle de longueur impaire supérieur à 4 ni complémentaire de cycle de longueur impaire supérieure à 4. Dans les années 60, Claude Berge a conjecturé que les graphes de Berge étaient des graphes parfaits. C'est-à-dire que la taille de la plus grande clique est exactement le nombre minimum de couleurs nécessaire à une coloration propre et ce pour tout sous-graphe. En 2002, Chudnovsky, Robertson, Seymour et Thomas ont démontré cette conjecture en utilisant un théorème de structure: les graphes de Berge sont basiques ou admettent une décomposition. Ce résultat est très utile pour faire des preuves par induction. Cependant, une des décompositions du théorème, la skew-partition équilibrée, est très difficile à utiliser algorithmiquement. Nous nous focalisons donc sur les graphes de Berge apprivoisés, c'est-à-dire les graphes de Berge sans skew-partition équilibrée. Pour pouvoir faire des inductions, nous devons adapter le théorème destructure de Chudnovsky et al à notre classe. Nous prouvons un résultat plus fort: les graphes de Berge apprivoisés sont basiques ou admettent une décomposition telle qu'un côté de la décomposition soit toujours basique. Nous avons de plus un algorithme calculant cette décomposition. Nous utilisons ensuite notre théorème pour montrer que les graphes de Berge apprivoisés admettent la propriété du grand biparti, de la clique-stable séparation et qu'il existe un algorithme polynomial permettant de calculer le stable maximum
Reconfiguration problems in graphs by Paul Ouvrard( )

1 edition published in 2021 in English and held by 1 WorldCat member library worldwide

In this thesis, we are interested in graph theory, and more specifically in reconfiguration problems. The goal of this area is to study the relationship between the feasible solutions of a given combinatorial optimization problem.Typically, is it possible to find a step-by-step transformation between two solutions thanks to an elementary operation?The original problem of this thesis is the so-called Dominating Set problem, which consists in finding a subset D of vertices such that each vertex either belongs to D or is adjacent to a vertex in D. We study the reconfiguration of dominating sets under two different elementary operations, mainly from an algorithmic point of view. We also provide necessary and sufficient conditions to ensure that a transformation always exists between two given solutions. Finally, we are interested in the parameterized complexity of an optimization variant: given a dominating set D, what is the smallest dominating set that is reachable from D under certain constraints?We are also interested in two other reconfiguration problems. First, we study the complexity of spanning trees reconfiguration with some constraints with respect to the minimum number of leaves. Finally, we introduce recoloring in the LOCAL model in Distributed Computing. In this last problem, we seek to optimize both the number of communication rounds and the number of steps between the two colorings
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1 edition published in 2017 in English and held by 1 WorldCat member library worldwide

Rooted structures in graphs : a project on Hadwiger's conjecture, rooted minors, and Tutte cycles by Samuel Mohr( )

1 edition published in 2020 in English and held by 1 WorldCat member library worldwide

Hadwigers Vermutung ist eine der anspruchsvollsten Vermutungen für Graphentheoretiker und bietet eine weitreichende Verallgemeinerung des Vierfarbensatzes. Ausgehend von dieser offenen Frage der strukturellen Graphentheorie werden gewurzelte Strukturen in Graphen diskutiert. Eine Transversale einer Partition ist definiert als eine Menge, welche genau ein Element aus jeder Menge der Partition enthält und sonst nichts. Für einen Graphen G und eine Teilmenge T seiner Knotenmenge ist ein gewurzelter Minor von G ein Minor, der T als Transversale seiner Taschen enthält. Sei T eine Transversale einer Färbung eines Graphen, sodass es ein System von kanten-disjunkten Wegen zwischen allen Knoten aus T gibt; dann stellt sich die Frage, ob es möglich ist, die Existenz eines vollständigen, in T gewurzelten Minors zu gewährleisten. Diese Frage ist eng mit Hadwigers Vermutung verwoben: Eine positive Antwort würde Hadwigers Vermutung für eindeutig färbbare Graphen bestätigen. In dieser Arbeit wird ebendiese Fragestellung untersucht sowie weitere Konzepte vorgestellt, welche bekannte Ideen der strukturellen Graphentheorie um eine Verwurzelung erweitern. Beispielsweise wird diskutiert, inwiefern hoch zusammenhängende Teilmengen der Knotenmenge einen hoch zusammenhängenden, gewurzelten Minor erzwingen. Zudem werden verschiedene Ideen von Hamiltonizität in planaren und nicht-planaren Graphen behandelt
Problèmes de placement, de coloration et d'identification by Petru Valicov( )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

In this thesis we study three theoretical computer science problems, namely the orthogonal packing problem (OPP for short), strong edge-colouring and identifying codes.OPP consists in testing whether a set of rectangular items can be packed in a rectangular container without overlapping and without exceeding the borders of this container. An additional constraint is that the rotation of the items is not allowed. The problem is NP-hard even when the problem is reduced to packing squares in a square. We propose an exact algorithm for solving OPP efficiently using the characterization of the problem by interval graphs proposed by Fekete and Schepers. For this purpose we use some compact representation of interval graphs - MPQ-trees. We show experimental results of our approach by comparing them to the results of other algorithms known in the literature. we observe promising gains.The study of strong edge-colouring and identifying codes is focused on the structural and computational aspects of these combinatorial problems. In the case of strong edge-colouring we are interested in the families of planar graphs and subcubic graphs. We show optimal upper bounds for the strong chromatic index of subcubic graphs as a function of the maximum average degree. We also show that every planar subcubic graph without induced cycles of length 4 and 5 can be strong edge-coloured with at most nine colours. Finally, we confirm the difficulty of the problem by showing that it remains NP-complete even in some restricted classes of planar subcubic graphs.For the subject of identifying codes we propose a characterization of non-trivial graphs having maximum identifying code number ID, that is n-1, where n is the number of vertices. We study the case of line graphs and prove lower and upper bounds for ID parameter in this class. At last we investigate the complexity of the corresponding decision problem and show the existence of a linear algorithm for computing ID of the line graph L(G) where G has the size of the tree-width bounded by a constant. On the other hand, we show that the identifying code problem is NP-complete in various subclasses of planar graphs
Etude d'une nouvelle classe de graphes : les graphes hypotriangulés by Hélène Topart( )

1 edition published in 2011 in French and held by 1 WorldCat member library worldwide

Dans cette thèse, nous définissons une nouvelle classe de graphes : les graphes hypotriangulés. Les graphes hypotriangulés vérifient que pour tout chemin de longueur deux, il existe une arête ou un autre chemin de longueur deux entre ses extrémités. Cette classe permet par exemple de modéliser des réseaux robustes. En effet, nous montrons que dans de tels graphes, la suppression d'une arête ou d'un sommet ne modifie pas la distance initiale entre toutes paires de sommets non adjacents. Ensuite, nous étudions et démontrons plusieurs propriétés pour cette classe de graphes. En particulier, après avoir introduit une famille de partitions spécifiques, nous montrons les relations entre certains éléments de cette famille et leur caractère hypotriangulé. De plus, grâce à ces partitions, nous caractérisons les graphes hypotriangulés minimum, qui, parmi les graphes hypotriangulés connexes, minimisent le nombre d'arêtes pour un nombre de sommets fixés.Dans une deuxième partie, nous étudions la complexité, pour la classe des graphes hypotriangulés, de problèmes difficiles dans le cas général. Nous montrons d'abord que les problèmes classiques de cycle hamiltonien, coloration, clique maximum et stable maximum restent NP-difficiles pour cette classe de graphes. Ensuite, nous nous intéressons à des problèmes de modification de graphes, pour lesquels il s'agit de déterminer le nombre minimal d'arêtes à ajouter ou supprimer à un graphe pour obtenir un graphe hypotriangulé : nous montrons la complexité de ces problèmes pour plusieurs classes de graphes
Algorithmes et résultats de complexité pour des problèmes de graphes avec contraintes additionnelles by Alexis Cornet( )

1 edition published in 2018 in French and held by 1 WorldCat member library worldwide

Les problèmes de domination (dominant, dominant indépendant, ...) et de couverture (vertex-cover, arbre de Steiner, ...) sont NP-complets. Pour autant, pour la plupart de ces problèmes, il existe toujours une solution constructible en temps polynomial (potentiellement de valeur objective très mauvaise), ou au moins, il est possible de déterminer facilement (en temps polynomial) l'existence ou non d'une solution. Ces problèmes, initialement issus de situations réelles, sont des modélisations simplistes de ces situations. Nous ajoutons donc des contraintes additionnelles modélisant des contraintes pratiques plausibles : les conflits, des paires d'éléments ne pouvant faire simultanément partie d'une solution (modélisant des incompatibilités diverses), la connexité dans un second graphe (les éléments doivent pouvoir communiquer, et le graphe correspondant à ces liens de communication n'est pas forcément le même) et les obligations, des sous-ensembles d'éléments interdépendants devant être ajoutés simultanément à une solution. Notre but ici n'est pas de modéliser un problème réel précis, mais d'étudier la manière dont ces contraintes modifient la complexité des problèmes étudiés. Nous verrons que dans un grand nombre de cas, déterminer l'existence même d'une solution devient difficile, même sans se préoccuper de leur optimisation. Le problème du firefighter modélise des pompiers tentant de contenir un feu se propageant au tour par tour dans un graphe (potentiellement infini). Nous avons étudié ce problème en ajoutant des contraintes sur le déplacement des pompiers (une vitesse de déplacement limitée entre deux tours). Nous verrons que ces contraintes augmentent en général le nombre de pompiers nécessaires mais ne provoquent pas de changements aussi importants que dans les problèmes précédents
Width Parameters on Even-Hole-Free Graphs by Ni Luh Dewi Sintiari( )

1 edition published in 2021 in English and held by 1 WorldCat member library worldwide

Un trou dans un graphe est un cycle sans corde d'une longueur au moins quatre. Un graphe est sans trou pair s'il ne contient aucun trou de longueur paire comme sous-graphe induit (où un sous-graphe est induit s'il peut être obtenu en supprimant des sommets du graphe d'origine). La première étude structurelle majeure de cette classe de graphes a été réalisée par Conforti, Cornuéjols, Kapoor et Vušković (2002), où leur motivation première était de développer des techniques qui peuvent ensuite être utilisées dans l'étude des graphes parfaits. En effet, la technique de décomposition qui a été développée lors de l'étude des graphes sans trous pairs a conduit à la preuve de la célèbre conjecture des graphes parfaits de Chudnovsky, Seymour, Robertson et Thomas (prouvée en 2002). Des études montrent que ces classes de graphes ont une structure similaire en termes de théorème de décomposition. Cependant, alors que de nombreux problèmes d'optimisation tels que la coloration des graphes et les problèmes d'ensembles indépendants maximaux peuvent être résolus en temps polynomial pour des graphes parfaits, la complexité est inconnue pour les graphes sans trous pairs. Le but de cette thèse est d'avoir une meilleure compréhension de la structure des graphes sans trous pairs. Pour cela, nous étudions certains paramètres de largeur de graphes sans trous pairs, en particulier la largeur d'arbre (ou tree-width). La tree-width est un nombre associé à un graphe afin de mesurer à quel point le graphe est proche d'être un arbre. Intuitivement, une petite tree-width signifie que le graphe a une structure proche de celle d'un arbre, tandis qu'une tree-width grande signifie que la structure est plus complexe. En général, la tree-width des graphes sans trous pairs est illimitée car les graphes complets sont sans trous pairs. Mais il existe des graphes sans trous pairs avec une tree-width limitée par une constante ou par une fonction de son nombre de clique. Cela se produit lorsque certaines structures sont exclues, par exemple lorsque les graphes sont planaires, ou sans triangle, ou ne contiennent pas de sous-graphe induit isomorphe à un poêle (un trou avec une arêtes supplémentaire), ou une casquette (un trou avec un sommet qui est adjacent à deux sommets du trou qui sont de distance deux). Dans cette thèse, nous montrons que les graphes sans clique de taille quatre peuvent avoir une tree-width arbitrairement grande, répondant négativement à une question de Cameron, Chaplick et Hoàng (2018). Pour la preuve, nous définissons une famille de graphes sans trous pairs et sans clique de taille quatre qui ont une tree-width arbitrairement grande. Motivés par ce résultat, nous découvrons d'autres sous-classes de graphes sans trous pairs ayant une tree-width bornée
Matrix decompositions and algorithmic applications to (hyper)graphs by Benjamin Bergougnoux( )

1 edition published in 2019 in English and held by 1 WorldCat member library worldwide

Classes héréditaires de graphes : de la structure vers la coloration by Cléophée Robin( )

1 edition published in 2021 in English and held by 1 WorldCat member library worldwide

This thesis deals with the structure of some hereditary classes of graphs. A class of graphs is hereditary if it is closed under vertex deletion. A better understanding of the structure of graphs contained in certain hereditary classes sometime yields results on optimisation problems such as the coloring problem. We focus on three hereditary classes, the first being a subclass of even-hole-free graphs and the other two being minimal open cases for the complexity of the coloring problem when restricted to classes defined by excluding subgraphs of order 4.First we provide a structural result for the class of graphs Ck that is the class of graphs where every hole has length k. Using earlier results on other related classes of graphs, we obtain a structural theorem for the graphs in Ck when k is odd and at least 7. The theorem states that a graph in Ck with no clique cutset and no universal vertex is either a ring or belongs to a new class of graphs named blowup of template that we fully described.Secondly, we study the structure of graphs in Free{C4, 4K1}. We first focus on fixers. A graph H in Free{C4, 4K1} is a fixer if any graph in Free{C4, 4K1} containing H as an induced subgraph is an extended proper blowup of H. We prove that the icosahedron is a fixer. In addition the icosahedron minus one vertex has a similar property. It follows that graphs in Free{C4,4K1} that contain an icosahedron minus one vertex have bounded clique-width and can be colored in polynomial time. We provide a program that computes all fixers of small fixed order. Next we observe that for any graph G in Free{C4,4K1}, every subgraph of G induced by two disjoint cliques is a half graph. We give some thoughts on the study of the structure of graphs in Free{C4, 4K1} whose vertex sets can be partitioned into 3 cliques.The last class that we are interested in, is the class of antiprismatic graphs. We prove that the coloring problem is polynomial-time solvable when restricted to non-orientable antiprismatic graphs. The proof is largely based on the structural result provided by Chudnovsky and Seymour on the complement class: the prismatic graphs. Using this result, we prove that every non-orientable prismatic graph has at most 10 pairwise disjoint triangles. This yields a O(n7.5) algorithm that solves the clique cover problem in non-orientable prismatic graph. We also give an O(n5) algorithm for solving the problem of finding a maxi- mum number of vertex-disjoint triangles in both orientable and non-orientable prismatic graphs
 
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English (15)

French (7)