Philippe Meurdesoif

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When a column generation approach is applied to decomposable mixed integer programming problems, it is standard to formulate and solve the master problem as a linear program. Seen in the dual space, this results in the algorithm known in the nonlinear programming community as the cutting-plane algorithm of Kelley and Cheney-Goldstein. However, more stable(More)
We observe that ω(G) + χ(S( G)) = n = ω(S( G)) + χ(G) for any graph G with n vertices, where G is any acyclic orientation of G and where S( G) is the (complement of the) auxiliary line graph introduced in [1]. (Where as usual, ω and χ denote the clique number and the chromatic number.) It follows that, for any graph parameter β(G) sandwiched between ω(G)(More)
If G is a triangle-free graph, then two Gallai identities can be written as α(G)+ χ(L(G)) = |V (G)| = α(L(G))+ χ(G), where α and χ denote the stability number and the clique-partition number, and L(G) is the line graph of G. We show that, surprisingly, both equalities can be preserved for any graph G by deleting the edges of the line graph corresponding to(More)
In this paper we will describe a new class of coloring problems, arising from military frequency assignment, where we want to minimize the number of distinct n-uples of colors used to color a given set of n-complete-subgraphs of a graph. We will propose two relaxations based on Semi-Definite Programming models for graph and hypergraph coloring, to(More)
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