An algorithm for coloring some perfect graphs.

Discrete Mathematics (Impact Factor: 0.58). 01/1998; 183:1-16. DOI: 10.1016/S0012-365X(97)00082-4
Source: DBLP

ABSTRACT We propose a sequential method with 3-chromatic interchange for coloring perfect graphs.

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    ABSTRACT: In this note, the authors generalize the ideas presented by A. Tucker in his proof of the SPGC for K 4 Gamma e-free graphs in order to find a vertex v (called here a Tucker vertex) in G whose special neighborhood allows to extend a previous coloring of G Gamma v. The search of such a vertex led us to define a property on the intersection of large cliques and a family of classes of graphs that satisfy this property. We prove that every graph G in this family has a Tucker vertex and we use this fact to give a polynomial-time algorithm to compute !(G). We give a proof of the SPGC for a new class: graphs where every edge of a maximal clique of size at least 4 belongs to precisely that clique. The proof directly yields a combinatorial polynomial-time algorithm for coloring perfect graphs in this new class with the size of a maximum clique colors. Key words: Perfect graphs, vertex-coloring algorithms, Tucker vertex. 1 Introduction A graph G is perfect if, for each induced subgraph H of G...


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