On the complexity of vertex-coloring edge-weightings
暂无分享,去创建一个
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.
[1] Bruce A. Reed,et al. Vertex-Colouring Edge-Weightings , 2007, Comb..
[2] Bruce A. Reed,et al. Degree constrained subgraphs , 2005, Discret. Appl. Math..
[3] A. Thomason,et al. Edge weights and vertex colours , 2004 .
[4] Florian Pfender,et al. Vertex-coloring edge-weightings: Towards the 1-2-3-conjecture , 2010, J. Comb. Theory B.
[5] Qinglin Yu,et al. On vertex-coloring 13-edge-weighting , 2008 .