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Graphs which are vertex-critical with respect to the edge-chromatic number

Published online by Cambridge University Press:  24 October 2008

A. J. W. Hilton  and
P. D. Johnson
A. J. W. Hilton
Affiliation:
Department of Mathematics, University of Reading, Reading RG6 2AX
P. D. Johnson
Affiliation:
Department of Algebra, Combinatorics and Analysis, Auburn University, Auburn, AL 36849, U.S.A.
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Extract

In this paper, multigraphs will have no loops. For a multigraph G, the least number of colours needed to colour the edges of G in such a way that no two edges on the same vertex of G have the same colour, is called the edge-chromatic number, or the chromatic index, of G, and denoted χ′(G). It is clear that if Δ(G) denotes the maximum degree of G, then Δ(G) ≤ χ′(G). If Δ(G) = χ′(G), then G is Class 1, and otherwise G is Class 2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 2 , September 1987 , pp. 211 - 221
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

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