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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)

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)

- M Voigt
- 1998

We consider the following type of problems. Given a graph G = (V; E) and lists L(v) of allowed colors for its vertices v 2 V such that jL(v)j = p for all v 2 V and jL(u) \ L(v)j c for all uv 2 E, is it possible to nd a \list coloring", i.e., a color f (v) 2 L(v) for each v 2 V , so that f (u) 6 = f (v) for all uv 2 E ? We prove that every graph of maximum… (More)

- Peter Mihh, Zsolt Tuza, Margit Voigt
- 1998

The choice ratio of a graph G = (V; E) is the minimum quotient a=b with the following property. For every assignment of a-element sets L(v) to the vertices v 2 V , there can be chosen b-element subsets C (v) L(v) for all v in such a way that C (v) \ C (v 0) = ; holds for every adjacent vertex pair v; v 0 .] proved that the choice ratio is equal to the… (More)