In: Discrete Mathematics, 2012, vol. 312, no. 10, p. 1838-1843
In threshold graphs one may find weights for the vertices and a threshold value t such that for any subset S of vertices, the sum of the weights is at most the threshold t if and only if the set S is a stable (independent) set. In this note we ask a similar question about vertex colorings: given an integer p, when is it possible to find weights (in general depending on p) for the vertices and a...
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In: Discrete Mathematics, 2010, vol. 310, p. 132-146
Given an undirected graph G=(V,E) with matching number \nu(G), a d-blocker is a subset of edges B such that \nu(/V,E\B))= d. While the associated decision problem is NP-complete in bipartite graphs we show how to construct efficiently minimum d-transversals and minimum d-blockers in the...
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