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L-Factors and Adjacent Vertex-Distinguishing Edge-Weighting

Published online by Cambridge University Press:  28 May 2015

Yinghua Duan ,
Hongliang Lu  and
Qinglin Yu
Yinghua Duan*
Affiliation:
Department of Mathematics, Beijing National Day School, Beijing, PR China
Hongliang Lu*
Affiliation:
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, PR China
Qinglin Yu*
Affiliation:
Department of Mathematics and Statistics, Thompson Rivers University, Kamloops, BC, Canada
*
Corresponding author. Email: yinghua115@mail.nankai.edu.cn
Corresponding author. Email: luhongliang215@sina.com
Corresponding author. Email: yu@tru.ca
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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.

Keywords

05C7005C15Edge-weightingvertex-coloringL-factor
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 2 , Issue 2 , May 2012 , pp. 83 - 93
Copyright
Copyright © Global-Science Press 2012

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