Improved bounds for the chromatic index of graphs and multigraphs

Applied Mathematics Letters

2008

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“…Hakimi and Schmeichel [5] showed that the edge-orderability and the HR-removability were in fact equivalent as follows.…”

Section: Resultsmentioning

confidence: 99%

“…Actually, our results in this work cover the results of Hoffman and Rodger [6] and Hakimi and Schmeichel [5] based on the core of G, which insure that G is of class 1.…”

mentioning

confidence: 99%

Some graphs of class 1 for f-colorings

Applied Mathematics Letters

2008

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Equitable edge-colorings of simple graphs

2010

J. Graph Theory

An edge-coloring of a graph G is equitable if, for each v ∈ V (G), the number of edges colored with any one color incident with v differs from the number of edges colored with any other color incident with v by at most one. A new sufficient condition for equitable edge-colorings of simple graphs is obtained. This result covers the previous results, which are due to Hilton and de Werra, verifies a conjecture made by Hilton recently, and substantially extends it to a more general class of graphs. ᭧

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f-Colorings of some graphs of f-class 1

Acta. Math. Sin.-English Ser.

2008