L-factors and adjacent vertex-distinguishing edge-weighting

Details L-factors and adjacent vertex-distinguishing edge-weighting L-factors and adjacent vertex-distinguishing edge-weighting

2010-07-08

arxiv.org/abs/1007.1295v1

Mathematics

Combinatorics

Scientific paper

An edge weighting problem of a graph G is an assignment of an integer weight to each edge e. Based on edge weighting problem, several types of vertex-coloring problems are put forward. A simple observation illuminates that edge weighting problem has a close relationship with special factors of graphs. In this paper, we obtain several results on the existence of factors with the pre-specified degrees, which generalizes earlier results in [2, 3]. Using these results, we investigate edge-weighting problem. In particular, we prove that every 4-colorable graph admits a vertex-coloring 4-edge-weighting.

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