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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} n and R be any polytope contained in [0, 1] n with R ∩ {0, 1} n = 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(More)
A graph G is said to be a Seymour 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)
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)
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