Year: 2012
East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 2 : pp. 83–93
Abstract
An edge-weighting problem of a graph G is an assignment of an integer weight to each edge e. Based on an edge-weighting problem, several types of vertex-coloring problems are put forward. A simple observation illuminates that the edge-weighting problem has a close relationship with special factors of the graphs. In this paper, we generalise several earlier results on the existence of factors with pre-specified degrees and hence investigate the edge-weighting problem — and in particular, we prove that every 4-colorable graph admits a vertex-coloring 4-edge-weighting.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.080411.291211a
East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 2 : pp. 83–93
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Edge-weighting vertex-coloring L-factor.