Plummer, M. D.Overview
Most widely held works by
M. D Plummer
Matching theory
by László Lovász
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27 editions published between 1986 and 2009 in English and Undetermined and held by 581 WorldCat member libraries worldwide This study of matching theory deals with bipartite matching, network flows, and presents fundamental results for the nonbipartite case. It goes on to study elementary bipartite graphs and elementary graphs in general. Further discussed are 2matchings, general matching problems as linear programs, the Edmonds Matching Algorithm (and other algorithmic approaches), ffactors and vertex packing
Degree sums, neighborhood unions and matching extension in graphs
by M. D Plummer
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1 edition published in 1990 in English and held by 3 WorldCat member libraries worldwide
Some results on K(r)covered graphs
by Odile Favaron
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1 edition published in 1996 in English and held by 3 WorldCat member libraries worldwide
Cycles through specified vertices in 3connected cubic graphs
by Derek Allan Holton
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1 edition published in 1979 in English and held by 3 WorldCat member libraries worldwide
A corollary to Perfect's Theorem
by Derek Allan Holton
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1 edition published in 1981 in English and held by 3 WorldCat member libraries worldwide
Some recent results on cycle traversability in graphs
by M. D Plummer
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1 edition published in 1981 in English and held by 2 WorldCat member libraries worldwide
On bicritical graphs
by László Lovász
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2 editions published in 1973 in English and held by 2 WorldCat member libraries worldwide
Extending Matchings in Planar Graphs 4
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1 edition published in 1989 in English and held by 1 WorldCat member library worldwide The structure of certain non2extendable planar graphs is studied first. In particular, 4connected 5regular planar graphs which are not 2extendable are investigated and examples of these are presented. It is then proved that all 5connected even planar graphs are 2extendable. Finally, a certain configuration called a generalized butterfly is defined and it is shown that 4connected maximal planar even graphs which contain no generalized butterfly are 2extendable
WellCovered Graphs: A Survey
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1 edition published in 1991 in English and held by 1 WorldCat member library worldwide A graph G is wellcovered (or wc) if every maximal independent set of points in G is also maximum. Clearly, this is equivalent to the property that the greedy algorithm for constructing a maximal independent set always results in a maximum independent set. Although the problem of independence number is wellknown to be NPcomplete, it is trivially polynomial for well covered graphs. The concept of wellcoveredness was introduced by the author in PI and was first discussed therein with respect to its relationship to a number of other properties involving the independence number. Since then, a number of results about wellcovered graphs have been obtained. It is our purpose in this paper to survey these results for the first time. As the reader will see, many of the results we will discuss are quite recent and have not as yet appeared in print
Introduction and Terminology 2Extendability in 3Polytopes
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1 edition published in 1985 in English and held by 1 WorldCat member library worldwide Suppose G is a graph with p points and let n be a positive integer such that P> or = 2n + 2. Graph G is said to be nextendable if every matching of size n in G extends to a perfect matching. A graph G is called bicritical if G  u  v has a perfect matching, for all pairs of points u, v epsilon V (G). In a canonical decomposition theory for graphs in terms of their maximum (or, when present, perfect) matchings is discussed at length. Bicritical graphs play an important roll in this theory. In particular, those bicritical graphs which are 3connected (the socalled bricks) currently represent the atoms of the decomposition theory in that no further decomposition of these graphs has been obtained as yet. Indeed at present we seem far from an understanding of the structure of bicritical graphs or even that of bricks. Although interesting in its own right, the study of nextendability became more important when in a previous document it was shown that every 2extendable nonbipartite graph is a brick and that, for n> or = 2, every nextendable graph is also (n1)extendable. Thus we have available for study a nested set of subcollections of bicritical graphs
Some Recent Results on Graph Matching
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1 edition published in 1987 in English and held by 1 WorldCat member library worldwide A matching in a graph G is a set of lines, no two of which share a common point. A matching is perfect if it spans V(G). The problem of finding a matching of maximum cardinality in a graph models a number of significant realworld problems and, in addition, is of considerable mathematical interest in its own right. Matchings are in a sense among the best understood graphtheoretic objects: there exist efficient algorithms to find and good characterizations for the existence of perfect matchings and for the maximum weight of a matching; there are nice descriptions of polyhedra associated with matchings; good bounds and, for a few special classes, exact formulas for the number of perfect matchings in a graph. But there are many important questions that remain unanswered. What is the number of perfect matchings in a general graph? Which graphs can be written as the disjoint union of perfect matchings (i.e., which rregular graphs are rlinecolorable)? How does one generate a random perfect matching? Matching theory has often been in the front lines of research in graph theory and many results in matching theory have served as pilot results for new branches of study in combinatorics (e.g., minimax theorems, good characterizations and polyhedral descriptions)
On the Cyclability of kConnected (k+1)Regular Graphs
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1 edition published in 1986 in English and held by 1 WorldCat member library worldwide In the past fifteen years or so, there have been quite a number of papers dealing with variations on the following general theme. Given a graph G and a positive integer m, m <or = /V(G), find nontrivial conditions on G which will guarantee that given a set S = (v sub 1, ..., v sub m)  V(G), there exists a cycle C sub S containing S. In the special case m = /V(G), this documents deals with conditions for the existence of Hamiltonian cycles, in itself a subject studied extensively by many graph theorists
A Theorem on Matchings in the Plane. 2. Some Planar Considerations
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1 edition published in 1985 in English and held by 1 WorldCat member library worldwide Let G be a graph with (V(G)) = p points and (E(G)) = q lines. A matching in G is any set of lines in E(G) no two of which are adjacent. Matching M in G is said to be a perfect matching, or p.m., if every point of G is covered by a line of M. Let G be any graph with a perfect matching and suppose positive integer n <or minus (p  2)/2. Then G is n extendable if every matching in G containing n lines is a subset of a p.m. The concept of nextendability gradually evolved from the study of elementary bipartite graphs (which are 1extendable) and then of arbitrary 1extendable (or 'matchingcovered') graphs. The study of nextendability for arbitrary n was begun by the author (1980). This paper is concerned with matchings in planar graphs. When we speak of an imbedding of planar graph G in the plane, we mean a topological imbedding in the usual sense and would remind the reader that such an imbedding is necessarily 2cell. If we wish to refer to a planar graph G together with an imbedding of G in the plane, we shall speak of the plane graph G. The main result of this paper is to show that no planar graph is 3extendable
On the 2Extendability of Planar Graphs
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1 edition published in 1989 in English and held by 1 WorldCat member library worldwide Some sufficient conditions for the 2extendability of kconnected kregular (k > or = 3) planar graphs are given. In particular, it is proved that for k > or = 3, a kconnected kregular planar graph with each cyclic cutset of sufficiently large size is 2extendable. All graphs in this paper are finite, undirected, connected and simple, although some parallel edge situations will occur after some contractions are made. However, any loops formed by these contractions will be deleted. Let nu and n be positive integers with n < or = (v  2)/2 and let G be a graph with nu vertices and epsilon edges having a perfect matching. The graph G is said to be nextendable if every matching of size n in G lies in a perfect matching of G
Matching Extension and the Genus of a Graph
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1 edition published in 1986 in English and held by 1 WorldCat member library worldwide Let G be a graph with p points having a perfect matching and suppose n is a positive integer with n <or = (p2)/2. Then G is nextendable if every matching in G containing n lines is a subset of a perfect matching. In this paper we obtain an upper bound on the nextendability of a graph in terms of its genus. Keywords: Euler contributions; Theorems. (Author)
Matching Extension in Regular Graphs
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1 edition published in 1989 in English and held by 1 WorldCat member library worldwide This paper deals with extending matching in regular graphs. There are two main results. The first presents a sufficient condition in terms of cyclic connectivity for extending matching in regular bipartite graphs. This theorem generalizes an earlier result due to Holton and the author. The second result deals with regularbut not necessarily bipartitegraphs. In this case, it is known that a result analogous to that obtained in the bipartite case is impossible, but a new proof is given of a result of Naddef and Pulleyblank which guarantees that a regular graph with an even number of points which has sufficiently large cyclic connectivity will be bicritical. Algorithms. (jes)
Cyclic Coloration of 3Polytopes
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1 edition published in 1985 in English and held by 1 WorldCat member library worldwide This paper, all graphs will be finite, loopless and will have no parallel lines. Let G be a 2connected planar graph with <V(G)>=p points. Suppose G has some fixed imbedding Phi: G approaches Rsq in the plane. The pair (G Phi) is often called a plane graph. A cyclic coloration of (G Phi) is an assignment to colors to the points of G such that for any facebounding cycle F of (G Phi), the points of F have different colors. The cyclic coloration number chi sub c ((G Phi)) is the minimum number of colors in any cyclic coloration of (G, Phi). The main result of the present paper is to show that if (G, Phi) is a 3connected plane graph, then chi sub c (G, Phi) <p* (G, Phi)+ 9. Moreover, if rho* is sufficiently large of sufficiently large or sufficiently small, then this bound on chi sub c can be improved somewhat
Matching Extension in Bipartite Graphs. 1. Introduction and Terminology
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1 edition published in 1986 in English and held by 1 WorldCat member library worldwide All graphs in this paper will be finite and connected and will have no loops or parallel lines. Let n and p be positive integers with n <or = (p  2)/2 and let G be a graph with p points having a perfect matching. Graph G is said to be nextendable if every matching of size n in G extends to a perfect matching. This paper is concerned primarily with studying nextendability in bipartite graphs. In the first section of this paper the author gathers together the various characterizations of 1extendable bipartite graphs mentioned above and then give the natural generalizations to nextendability with a unified proof of the equivalencies. In another paper the author presented some results on the connectivity of general nextendable graphs. In the second section of this paper proves a result about connectivity which is peculiar to the bipartite case
Toughness and Matching Extension in Graphs
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1 edition published in 1986 in English and held by 1 WorldCat member library worldwide In the present paper, we wish to treat some relationships between toughness of a graph and the nextendability of the graph. We will prove two results. The first says essentially that if a graph has sufficiently high toughness (and has an even number of points) then it must be nextendable. The second result applies to graphs with toughness less than one and presents an upper bound on the value of n for which such a graph can be nextendable. In the final section, we compare and contrast these results with the nfactor results of Enomoto, Jackson, Katerinis and A. Saito
The Cartesian Product of a kExtendable and an lExtendable Graph is (k + l +1)Extendable
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1 edition published in 1991 in English and held by 1 WorldCat member library worldwide Let us start with the definition of a kappaextendable graph G. Suppose kappa is an integer such that 1 <or = kappa <or = (/V(G)/2)/2. A graph G is kappaextendable if G is connected, has a perfect matching (a 1 factor) and any matching in G consisting of kappa edges can be extended to (i.e., is a subset of) a perfect matching. The extendability number of G, extG, is the maximum kappa such that G is kappaextendable. A natural problem is to determine the extendability number of a graph G more
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Plummer, M.D.
Plummer, Michael D.
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