L-factors and adjacent vertex-distinguishing edge-weighting [article]

Yinghua Duan, Hongliang Lu, Qinglin yu
2010 arXiv   pre-print
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
more » ... problem. In particular, we prove that every 4-colorable graph admits a vertex-coloring 4-edge-weighting.
arXiv:1007.1295v1 fatcat:mwfmqzmowzgwxjm44ixbyy63be