Fulkerson, D. R.
Overview
Works:  116 works in 332 publications in 3 languages and 3,604 library holdings 

Roles:  Author, Editor, Contributor, Other 
Classifications:  QA265, 519.92 
Publication Timeline
.
Most widely held works by
D. R Fulkerson
Flows in networks by
Lester R Ford(
Book
)
70 editions published between 1962 and 2016 in 4 languages and held by 1,852 WorldCat member libraries worldwide
The techniques presented by Ford and Fulkerson spurred the development of powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming. In addition, the book helped illuminate and unify results in combinatorial mathematics while emphasizing proofs based on computationally efficient construction
70 editions published between 1962 and 2016 in 4 languages and held by 1,852 WorldCat member libraries worldwide
The techniques presented by Ford and Fulkerson spurred the development of powerful computational tools for solving and analyzing network flow models, and also furthered the understanding of linear programming. In addition, the book helped illuminate and unify results in combinatorial mathematics while emphasizing proofs based on computationally efficient construction
Studies in graph theory by
Claude Berge(
Book
)
9 editions published in 1975 in English and held by 652 WorldCat member libraries worldwide
9 editions published in 1975 in English and held by 652 WorldCat member libraries worldwide
Polyhedral combinatorics : dedicated to the memory of D.R. Fulkerson by
M. L Balinski(
Book
)
11 editions published in 1978 in English and Undetermined and held by 328 WorldCat member libraries worldwide
11 editions published in 1978 in English and Undetermined and held by 328 WorldCat member libraries worldwide
Minimal karc connected graph by
D. R Fulkerson(
Book
)
7 editions published between 1961 and 1971 in English and held by 49 WorldCat member libraries worldwide
A graph is karcconnected if it is necessary to remove at least k arcs in order to disconnect the graph. The paper solves the problem of determining the least number of arcs required in a karcconnected graph on n nodes by describing constructions that produce such graphs having kn/2 arcs (for kn even) or (kn+1)/2 arcs (for kn odd). These results have application to the practical problem of synthesizing minimum cost, kreliable communication networks. (Author)
7 editions published between 1961 and 1971 in English and held by 49 WorldCat member libraries worldwide
A graph is karcconnected if it is necessary to remove at least k arcs in order to disconnect the graph. The paper solves the problem of determining the least number of arcs required in a karcconnected graph on n nodes by describing constructions that produce such graphs having kn/2 arcs (for kn even) or (kn+1)/2 arcs (for kn odd). These results have application to the practical problem of synthesizing minimum cost, kreliable communication networks. (Author)
Blocking and antiblocking pairs of polyhedra by
D. R Fulkerson(
Book
)
4 editions published between 1969 and 1970 in English and held by 42 WorldCat member libraries worldwide
Some of the main notions and theorems about blocking pairs of polyhedra and antiblocking pairs of polyhedra are described. The two geometric duality theories conform in many respects, but there are certain important differences. Applications to various combinatorial extremum problems are discussed, and some classes of blocking and antiblocking pairs that have been explicitly determined are mentioned. (Author)
4 editions published between 1969 and 1970 in English and held by 42 WorldCat member libraries worldwide
Some of the main notions and theorems about blocking pairs of polyhedra and antiblocking pairs of polyhedra are described. The two geometric duality theories conform in many respects, but there are certain important differences. Applications to various combinatorial extremum problems are discussed, and some classes of blocking and antiblocking pairs that have been explicitly determined are mentioned. (Author)
Notes on combinatorial mathematics: antiblocking polyhedra by
Delbert Ray Fulkerson(
Book
)
5 editions published in 1970 in English and Undetermined and held by 42 WorldCat member libraries worldwide
A geometric duality theory of antiblocking pairs of polyhedra is developed and applied to a number of problems in extremal combinatorics. It is shown that antiblocking pairs are characterized by a minmax equality, the analogue of the maxflow mincut equality for blocking pairs of polyhedra, or by a maxmax inequality, the analogue of the lengthwidth inequality for blocking pairs of polyhedra. A main combinatorial result is that if A, B are (0,1)matrices defining an antiblocking pair of polyhedra, then the minmax equality holds for both ordered pairs A, B and B, A in a strong integer form. This theorem bears on a wellknown unsolved problem in graph theory, the perfect graph conjecture, and in fact proves what might be called the 'pluperfect' graph theorem. (Author)
5 editions published in 1970 in English and Undetermined and held by 42 WorldCat member libraries worldwide
A geometric duality theory of antiblocking pairs of polyhedra is developed and applied to a number of problems in extremal combinatorics. It is shown that antiblocking pairs are characterized by a minmax equality, the analogue of the maxflow mincut equality for blocking pairs of polyhedra, or by a maxmax inequality, the analogue of the lengthwidth inequality for blocking pairs of polyhedra. A main combinatorial result is that if A, B are (0,1)matrices defining an antiblocking pair of polyhedra, then the minmax equality holds for both ordered pairs A, B and B, A in a strong integer form. This theorem bears on a wellknown unsolved problem in graph theory, the perfect graph conjecture, and in fact proves what might be called the 'pluperfect' graph theorem. (Author)
Flots dans les graphes by
Lester Randolf Ford(
Book
)
1 edition published in 1967 in French and held by 36 WorldCat member libraries worldwide
1 edition published in 1967 in French and held by 36 WorldCat member libraries worldwide
Studies in graph theory by
D. R Fulkerson(
Book
)
7 editions published in 1975 in English and held by 34 WorldCat member libraries worldwide
7 editions published in 1975 in English and held by 34 WorldCat member libraries worldwide
Studies in graph theory by
D. R. ed Fulkenson(
Book
)
8 editions published in 1975 in English and held by 32 WorldCat member libraries worldwide
8 editions published in 1975 in English and held by 32 WorldCat member libraries worldwide
Subgraphs of bipartite and directed graphs by
Jon Folkman(
Book
)
5 editions published between 1965 and 1968 in English and held by 25 WorldCat member libraries worldwide
The main theorem of this study provides necessary and sufficient conditions for a locally finite bipartite graph to have a subgraph whose valences lie in prescribed intervals. The theorem is applied to the study of integervalued flows in locally finite directed graphs. In particular, generalizations of the maxflow mincut theorem and the circulation theorem are obtained. The axiom of choice is assumed throughout. (Author)
5 editions published between 1965 and 1968 in English and held by 25 WorldCat member libraries worldwide
The main theorem of this study provides necessary and sufficient conditions for a locally finite bipartite graph to have a subgraph whose valences lie in prescribed intervals. The theorem is applied to the study of integervalued flows in locally finite directed graphs. In particular, generalizations of the maxflow mincut theorem and the circulation theorem are obtained. The axiom of choice is assumed throughout. (Author)
Disjoint common partial transversals of two families of sets by
Delbert Ray Fulkerson(
Book
)
4 editions published between 1969 and 1970 in English and held by 24 WorldCat member libraries worldwide
The theory of flows in networks is applied to obtain necessary and sufficient conditions on two finite families of subsets of a finite set in order that there exist k mutually disjoint common partial transversals, each of size p, of the two families. (Author)
4 editions published between 1969 and 1970 in English and held by 24 WorldCat member libraries worldwide
The theory of flows in networks is applied to obtain necessary and sufficient conditions on two finite families of subsets of a finite set in order that there exist k mutually disjoint common partial transversals, each of size p, of the two families. (Author)
Blocking polyhedra by
D. R Fulkerson(
Book
)
5 editions published in 1968 in English and held by 23 WorldCat member libraries worldwide
A geometric theory of 'blocking polyhedra' is developed and applied to a number of problems in extremal combinatorics. The basic notion is a variant of the concept of polar polyhedra and exhibits a similar duality. The maxflow mincut equality and the lengthwidth inequality, valid for paths and cuts in a network, always hold for a blocking pair of polyhedra, and the former of these characterizes the blocking relation. A typical combinatorial application is a new geometric characterization of the permutation matrices as the extreme points of a certain unbounded convex polyhedron. (Author)
5 editions published in 1968 in English and held by 23 WorldCat member libraries worldwide
A geometric theory of 'blocking polyhedra' is developed and applied to a number of problems in extremal combinatorics. The basic notion is a variant of the concept of polar polyhedra and exhibits a similar duality. The maxflow mincut equality and the lengthwidth inequality, valid for paths and cuts in a network, always hold for a blocking pair of polyhedra, and the former of these characterizes the blocking relation. A typical combinatorial application is a new geometric characterization of the permutation matrices as the extreme points of a certain unbounded convex polyhedron. (Author)
Bottleneck extrema by
Jack Edmonds(
Book
)
5 editions published between 1965 and 1968 in English and held by 22 WorldCat member libraries worldwide
Bottleneck problems relate to matching input flow with production flow in order to optimize production. In this study, bottleneck extremum problems are established in their proper abstract setting, and a 'threshold method' for their solution is found. Several examples of blocking systems are also discussed. (Author)
5 editions published between 1965 and 1968 in English and held by 22 WorldCat member libraries worldwide
Bottleneck problems relate to matching input flow with production flow in order to optimize production. In this study, bottleneck extremum problems are established in their proper abstract setting, and a 'threshold method' for their solution is found. Several examples of blocking systems are also discussed. (Author)
Studies in graph theory(
Book
)
5 editions published in 1975 in English and Undetermined and held by 20 WorldCat member libraries worldwide
5 editions published in 1975 in English and Undetermined and held by 20 WorldCat member libraries worldwide
A Transportation program for filling idle classrooms in Los Angeles by
D. Ray Fulkerson(
Book
)
3 editions published in 1966 in English and held by 19 WorldCat member libraries worldwide
A citywide transportation model designed to fill vacant seats in elementary school classrooms with pupils voluntarily bused from overcrowded schools elsewhere. Basic requirements include minimum cost and minimum distance traveled (average travel time, one way, is 20 minutes). Data, working assumptions, detailed routing (with map), and cost estimates are presented. By transporting 10 percent of the pupils now on short sessions, the program would provide the equivalent of 72 new classrooms at a daily cost per child of 67 cents, while alleviating de facto segregation. (Prepared for presentation to the Los Angeles Board of Education by TransportAChild, a nonprofit educational foundation.)
3 editions published in 1966 in English and held by 19 WorldCat member libraries worldwide
A citywide transportation model designed to fill vacant seats in elementary school classrooms with pupils voluntarily bused from overcrowded schools elsewhere. Basic requirements include minimum cost and minimum distance traveled (average travel time, one way, is 20 minutes). Data, working assumptions, detailed routing (with map), and cost estimates are presented. By transporting 10 percent of the pupils now on short sessions, the program would provide the equivalent of 72 new classrooms at a daily cost per child of 67 cents, while alleviating de facto segregation. (Prepared for presentation to the Los Angeles Board of Education by TransportAChild, a nonprofit educational foundation.)
Networks, frames, blocking systems by
D R Fulkerson(
Book
)
3 editions published in 1967 in English and held by 17 WorldCat member libraries worldwide
A survey of some of the basic problems, theorems, and constructions for flow networks, and their extension to more general combinatorial structures. One generalization is that obtained by replacing the vertexedge incidence matrix of an oriented network by an arbitrary real matrix. This leads to the notion of a frame of a subspace of Euclidean nspace, a concept very closely allied to that of a real matric matroid. The treatment relates matroid theory and linear programming theory, and thus provides another viewpoint on linear programming, and in particular, on digraphoidprogramming. In addition, a very general combinatorial structure called a blocking system is given an axiomatic formulation. These systems have arisen in a variety of contexts, including multiperson game theory and abstract covering problems. It is shown that one of the network theorems surveyed in the study extends to all blocking systems, and indeed characterizes such systems
3 editions published in 1967 in English and held by 17 WorldCat member libraries worldwide
A survey of some of the basic problems, theorems, and constructions for flow networks, and their extension to more general combinatorial structures. One generalization is that obtained by replacing the vertexedge incidence matrix of an oriented network by an arbitrary real matrix. This leads to the notion of a frame of a subspace of Euclidean nspace, a concept very closely allied to that of a real matric matroid. The treatment relates matroid theory and linear programming theory, and thus provides another viewpoint on linear programming, and in particular, on digraphoidprogramming. In addition, a very general combinatorial structure called a blocking system is given an axiomatic formulation. These systems have arisen in a variety of contexts, including multiperson game theory and abstract covering problems. It is shown that one of the network theorems surveyed in the study extends to all blocking systems, and indeed characterizes such systems
Studies in graph theory(
Book
)
8 editions published in 1975 in English and Undetermined and held by 16 WorldCat member libraries worldwide
8 editions published in 1975 in English and Undetermined and held by 16 WorldCat member libraries worldwide
Transversal packings and covers by
D. R Fulkerson(
Book
)
2 editions published in 1965 in English and held by 15 WorldCat member libraries worldwide
Let S sub 1, S sub 2, S sub M be a collection of subsets of a finite set S. The subset T of S is a partial transversal of size t of the subsets S sub 1, S sub 2, S sub M if (i) T consists of t elements of S, and (ii) the term rank of the incidence matrix of S sub 1, S sub 2, S sub M vs. elements of T is equal to t. Necessary and sufficient conditions in order that S sub 1, S sub 2, S sub M have mutually disjoint partial transversals T sub 1, T sub 2, T sub P of sizes t sub 1, t sub 2, t sub P are known. This memorandum shows that the problem of constructing such a transversal packing can be formulated in terms of flows in networks, and existence conditions obtained from results in network flow theory. A similar approach is presented for an analogous covering problem involving partial transversals of prescribed sizes. Finally, connections are indicated between these problems and some recent results of Edmonds in matroid theory. (Author)
2 editions published in 1965 in English and held by 15 WorldCat member libraries worldwide
Let S sub 1, S sub 2, S sub M be a collection of subsets of a finite set S. The subset T of S is a partial transversal of size t of the subsets S sub 1, S sub 2, S sub M if (i) T consists of t elements of S, and (ii) the term rank of the incidence matrix of S sub 1, S sub 2, S sub M vs. elements of T is equal to t. Necessary and sufficient conditions in order that S sub 1, S sub 2, S sub M have mutually disjoint partial transversals T sub 1, T sub 2, T sub P of sizes t sub 1, t sub 2, t sub P are known. This memorandum shows that the problem of constructing such a transversal packing can be formulated in terms of flows in networks, and existence conditions obtained from results in network flow theory. A similar approach is presented for an analogous covering problem involving partial transversals of prescribed sizes. Finally, connections are indicated between these problems and some recent results of Edmonds in matroid theory. (Author)
Flows in networks, by L.R. Ford [and] D.R. Fulkerson by
L. R Ford(
Book
)
1 edition published in 1962 in English and held by 15 WorldCat member libraries worldwide
1 edition published in 1962 in English and held by 15 WorldCat member libraries worldwide
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Related Identities
 Ford, L. R. Author
 Ford, L. R. (Lester Randolph) 1927 Author
 Berge, Claude Other Author
 Hoffman, A. J. (Alan Jerome) 1924 Author Editor
 Balinski, M. L. Author Editor
 Rand Corporation
 Shapley, Lloyd S. 19232016
 Folkman, Jon Author
 Arinal, JeanClaude Translator
 RAND CORP SANTA MONICA CALIF
Useful Links
Associated Subjects
Busing for school integration CaliforniaLos Angeles Classroom utilization Combinatorial analysis EconomicsMathematical models Fulkerson, D. R Game theory Graph theory Linear programming Mathematics Matroids Maxima and minima Network analysis (Planning) PERT (Network analysis) Polyhedra Programming (Mathematics) System analysis
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Alternative Names
D. R. Fulkerson American mathematician
D. R. Fulkerson amerikansk matematikar
D. R. Fulkerson amerikansk matematiker
Delbert Ray Fulkerson Amerikaans wiskundige (19241976)
Delbert Ray Fulkerson matemático estadounidense
Delbert Ray Fulkerson mathématicien américain
Delbert Ray Fulkerson USamerikanischer Mathematiker
Falkerson, D. R. 19241976
Fulkerson, D. R.
Fulkerson, D. R. 19241976
Fulkerson, D. Ray 19241976
Fulkerson, Delbert R. 19241976
Fulkerson, Delbert Ray.
Fulkerson, Delbert Ray 19241976
Ray Fulkerson, Delbert 19241976
Делберт Рэй Фалкерсон американский математик
Фалкерсон, Д. Р..
دلبرت ری فولکرسون ریاضیدان آمریکایی
デルバート・ファルカーソン
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