Volume 2, Issue 2
L-Factors and Adjacent Vertex-Distinguishing Edge-Weighting

Yinghua Duan, Hongliang Lu & Qinglin Yu

East Asian J. Appl. Math., 2 (2012), pp. 83-93.

Published online: 2018-02

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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 vertexcoloring problems are put forward. A simple observation illuminates that the edgeweighting 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

Edge-weighting vertex-coloring L-factor

  • AMS Subject Headings

05C70 05C15

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-2-83, author = {Yinghua Duan, Hongliang Lu and Qinglin Yu}, title = {L-Factors and Adjacent Vertex-Distinguishing Edge-Weighting}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {2}, number = {2}, pages = {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 vertexcoloring problems are put forward. A simple observation illuminates that the edgeweighting 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.080411.291211a}, url = {http://global-sci.org/intro/article_detail/eajam/10868.html} }
TY - JOUR T1 - L-Factors and Adjacent Vertex-Distinguishing Edge-Weighting AU - Yinghua Duan, Hongliang Lu & Qinglin Yu JO - East Asian Journal on Applied Mathematics VL - 2 SP - 83 EP - 93 PY - 2018 DA - 2018/02 SN - 2 DO - http://dor.org/10.4208/eajam.080411.291211a UR - https://global-sci.org/intro/article_detail/eajam/10868.html KW - Edge-weighting KW - vertex-coloring KW - L-factor AB -

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 vertexcoloring problems are put forward. A simple observation illuminates that the edgeweighting 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.

Yinghua Duan, Hongliang Lu & Qinglin Yu. (1970). L-Factors and Adjacent Vertex-Distinguishing Edge-Weighting. East Asian Journal on Applied Mathematics. 2 (2). 83-93. doi:10.4208/eajam.080411.291211a
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