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the date of receipt and acceptance should be inserted later Abstract. 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… (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) and… (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… (More)

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