An algorithm for coloring some perfect graphs

University of Science and Technology Houari Boumediene, Le Retour de la Chasse, Alger, Algeria
Discrete Mathematics (Impact Factor: 0.56). 03/1998; 183(1-3):1-16. DOI: 10.1016/S0012-365X(97)00082-4
Source: DBLP


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

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Available from: Sylvain Gravier, Nov 03, 2014
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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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    ABSTRACT: We give a sequential algorithm to color a new class of perfect graphs. Our algorithm is based on a 3-chromatic exchange using Tucker's algorithm for 3-coloring the perfect graphs that do not contain a clique of size four.
    Discrete Mathematics 05/1999; 203(1-3):121-131. DOI:10.1016/S0012-365X(99)00023-0 · 0.56 Impact Factor
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    ABSTRACT: This paper surveys some of the main combinatorial methods for inferring patterns from a string, or a set of strings. The types of problems that will be addressed are repeat identification and common pattern inference. The strings that will concern us represent biological entities, nucleic acid and protein sequences or, in some cases, structures. As is well-known, exact ("identical") patterns hardly make sense in biology; we consider here two types of similar ("nonidentical") patterns. One comes from looking at what "hides" behind each letter of the dna/rna or protein alphabet while the other corresponds to the more familiar notion of "errors". The errors concern mutational events that may affect a molecule during dna replication.
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