Frontiers of Mathematics in China >
On vertex-coloring edge-weighting of graphs
Received date: 27 Nov 2008
Accepted date: 04 Dec 2008
Published date: 05 Jun 2009
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A k-edge-weightingw of a graph G is an assignment of an integer weight, w(e) ∈ {1, …, k}, to each edge e. An edge-weighting naturally induces a vertex coloring c by defining for every u ∈ V (G). A k-edge-weighting of a graph G is vertex-coloring if the induced coloring c is proper, i.e., c(u) ≠ c(v) for any edge uv ∈ E(G). When k ≡ 2 (mod 4) and k≥6, we prove that if G is k-colorable and 2-connected, δ(G)≥k - 1, then G admits a vertex-coloring k-edge-weighting. We also obtain several suffcient conditions for graphs to be vertex-coloring k-edge-weighting.
Key words： Vertex coloring; edge-weighting
Hongliang LU , Xu YANG , Qinglin YU . On vertex-coloring edge-weighting of graphs[J]. Frontiers of Mathematics in China, 2009 , 4(2) : 325 -334 . DOI: 10.1007/s11464-009-0014-8
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