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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)

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)

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)

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