Yohann Benchetrit

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The complexity of the matching polytope of graphs may be measured with the maximum length β of a starting sequence of odd ears in an ear-decomposition. Indeed, a theorem of Edmonds and Pulleyblank shows that its facets are defined by 2-connected factor-critical graphs, which have an odd ear-decomposition (according to a theorem of Lovász). In particular,(More)
It is an open question whether the chromatic number of t-perfect graphs is bounded by a constant. The largest known value for this parameter is 4, and the only example of a 4-critical t-perfect graph, due to Laurent and Seymour, is the complement of the line graph of the prism Π (a graph is 4-critical if it has chromatic number 4 and all its proper induced(More)
Let S ⊆ {0, 1} and R be any polytope contained in [0, 1] with R ∩ {0, 1} = S. We prove that R has bounded Chvátal-Gomory rank (CG-rank) provided that S has bounded pitch and bounded gap, where the pitch is the minimum integer p such that all p-dimensional faces of the 0/1-cube have a nonempty intersection with S, and the gap is a measure of the size of the(More)
A graph G is said to be aSeymour graph if for any edge set F there exist |F | pairwise disjoint cuts each containing exactly one element of F , provided for every circuit C of G the necessary condition |C∩F | ≤ |C \F | is satisfied. Seymour graphs behave well with respect to some integer programs including multiflow problems, or more generally odd cut(More)
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