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L-Factors and Adjacent Vertex-Distinguishing Edge-Weighting
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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.
Global Science Press
Title: L-Factors and Adjacent Vertex-Distinguishing Edge-Weighting
Description:
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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