On maximal independent sets of vertices in claw-free graphs
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Given a finite claw-free graph with real numbers assigned to the vertices, this work exhibits an algorithm for producing an independent set of vertices of maximum total weight, which is “efficient” in the sense of J. Edmonds.About:
This article is published in Journal of Combinatorial Theory, Series B.The article was published on 1980-06-01 and is currently open access. It has received 496 citations till now. The article focuses on the topics: Graph center & Independent set.read more
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The ellipsoid method and its consequences in combinatorial optimization
TL;DR: The method yields polynomial algorithms for vertex packing in perfect graphs, for the matching and matroid intersection problems, for optimum covering of directed cuts of a digraph, and for the minimum value of a submodular set function.
Book ChapterDOI
The maximum clique problem
TL;DR: A survey of results concerning algorithms, complexity, and applications of the maximum clique problem is presented and enumerative and exact algorithms, heuristics, and a variety of other proposed methods are discussed.
Journal ArticleDOI
The NP-completeness column: An ongoing guide
TL;DR: This is the fourteenth edition of a quarterly column that provides continuing coverage of new developments in the theory of NP-completeness, and readers who have results they would like mentioned (NP-hardness, PSPACE- hardness, polynomialtime-solvability, etc.), or open problems they wouldlike publicized, should send them to David S. Johnson.
Journal ArticleDOI
Algorithme de recherche d'un stable de cardinalite maximum dans un graphe sans etoile
TL;DR: Cette procedure est differente de celle de Minty laquelle commence par chercher s'il existe des chaines augmentantes de longueur trois ou cinq et ce par enumeration, and ensuite a construire pour chaque couple of sommets insatures non voisins, un graphe annexe and a y appliquer l'algorithme du couplage d'Edmonds afin of detecter l'.
Book ChapterDOI
The structure of claw-free graphs.
Maria Chudnovsky,Paul Seymour +1 more
TL;DR: It is shown that every connected claw-free graph can be obtained from one of the basic claw- free graphs by simple expansion operations.
References
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Book ChapterDOI
Paths, Trees, and Flowers
TL;DR: A graph G is a set of elements called vertices and a finite set of edges called edges such that each edge meets exactly two vertices, called the end-points of the edge as mentioned in this paper.
Journal ArticleDOI
Maximum matching and a polyhedron with 0,1-vertices
TL;DR: The emphasis in this paper is on relating the matching problem to the theory of continuous linear programming, and the algorithm described does not involve any "blind-alley programming" -which, essentially, amounts to testing a great many combinations.
Journal ArticleDOI
A characterization of comparability graphs and of interval graphs
P. C. Gilmore,Alan J. Hoffman +1 more
TL;DR: In this paper, the authors give a simple algorithm for directing all the edges of a comparability graph in such a way that the resulting graph partially orders its vertices, which they call comparability graphs.