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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2011

On the complexity of vertex-coloring edge-weightings

Abstract

Given a graph G = (V; E) and a weight function omega : E -\textgreater R, a coloring of vertices of G, induced by omega, is defined by chi(omega) (nu) = Sigma(e(sic)nu) omega (e) for all nu is an element of V. In this paper, we show that determining whether a particular graph has a weighting of the edges from \1, 2\ that induces a proper vertex coloring is NP-complete.
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Dates and versions

hal-00990502 , version 1 (13-05-2014)

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Andrzej Dudek, David Wajc. On the complexity of vertex-coloring edge-weightings. Discrete Mathematics and Theoretical Computer Science, 2011, Vol. 13 no. 3 (3), pp.45--50. ⟨10.46298/dmtcs.548⟩. ⟨hal-00990502⟩

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