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In this thesis we focus our attention on the stable set polytope of claw-free graphs. This problem has been open for many years and albeit all the efforts engaged during those last three years, it is still open. This does not mean that no progress has been ...
Graph Coloring is a very active field of research in graph theory as well as in the domain of the design of efficient heuristics to solve problems which, due to their computational complexity, cannot be solved exactly (no guarantee that an optimal solution ...
It is a long standing open problem to find an explicit description of the stable set polytope of claw-free graphs. Yet more than 20 years after the discovery of a polynomial algorithm for the maximum stable set problem for claw-free graphs, there is even n ...
The common point between the different chapters of the present work is graph theory. We investigate some well known graph theory problems, and some which arise from more specific applications. In the first chapter, we deal with the maximum stable set probl ...
This paper presents an approach to automatically extract and evaluate the ``stability'' of pronunciation variants (i.e., adequacy of the model to accommodate this variability), based on multiple pronunciations of each lexicon words and the knowledge of a r ...
The notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies. A lot of problems, which are in general NP-complete, can be solved in polynomial time for graphs with small treewidth. In the first part of this paper we presen ...
We consider the problem of partitioning the node set of a graph into p cliques and k stable sets, namely the (p,k)-coloring problem. Results have been obtained for general graphs \cite{hellcomp}, chordal graphs \cite{hellchordal} and cacti for the case whe ...
Combinatorial optimization problems related to permutations have been widely studied. Here, we consider different generalizations of the usual coloring problem in permutation graphs. A cocoloring is a partition of a permutation into increasing and decreasi ...
It is a long standing open problem to find an explicit description of the stable set polytope of claw-free graphs. Yet more than 20 years after the discovery of a polynomial algorithm for the maximum stable set problem for claw-free graphs, there is even n ...
We deal with non-rank facets of the stable set polytope of claw-free graphs. We extend results of Giles and Trotter [7] by (i) showing that for any nonnegative integer a there exists a circulant graph whose stable set polytope has a facet-inducing inequali ...
