Margit Voigt

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Computing the chromatic number of a graph is an NP-hard problem. For random graphs and some other classes of graphs, estimators of the expected chromatic number have been well studied. In this paper, a new 0–1 integer programming formulation for the graph coloring problem is presented. The proposed new formulation is used to develop a method that generates(More)
A graph G is (a, b)-choosable if for any assignment of a list of a colors to each of its vertices there is a subset of b colors of each list so that subsets corresponding to adjacent vertices are disjoint. It is shown that for every graph G, the minimum ratio a/b where a, b range over all pairs of integers for which G is (a, b)-choosable is equal to the(More)
Let G = (V,E) be a graph, let f : V (G)→ N, and let k ≥ 0 be an integer. A list-assignment L of G is a function that assigns to each vertex v of G a set (list) L(v) of colors: usually each color is a positive integer. We say that L is an f -assignment if |L(v)| = f(v) for all v ∈ V , and a k-assignment if |L(v)| = k for all v ∈ V . A coloring ofG is a(More)
A k-dominating set is a set D k V such that every vertex i 2 V nD k has at least k i neighbours in D k. The k-domination number k (G) of G is the cardinality of a smallest k-dominating set of G. For k 1 = ::: = kn = 1, k-domination corresponds to the usual concept of domination. Our approach yields an improvement of an upper bound for the domination number(More)
A graph G = (V, E ) with vertex set V and edge set E is called (a , b)-choosable ( a 2 2b) if for any collection {L(w)lv E V} of sets L(v ) of cardinality a there exists a collection {C(w)lv E V } of subsets C ( u ) c L(u),IC(v)l = b, such that C(V) n C(W) = 0 for all vw E E. Giving a partial solution to a problem raised by Erdos, Rubin, and Taylor in 1979,(More)