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Some remarks on a paper by Vizing on critical graphs

Published online by Cambridge University Press:  24 October 2008

Stanley Fiorini
Affiliation:
The Open University, Milton Keynes, Bucks, England

Abstract

In papers (7, 8), Vizing studied graphs which are critical with respect to edge colourings. In particular, he obtained bounds on the number of edges and on the circuit length of such graphs in terms of its maximum valency. The object of this paper is to improve these bounds by obtaining others which also take into account the order of the graph.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Beineke, L. W. and Wilson, R. J.On the edge-chromatic number of a graph. Discrete Math. 5 No. 1 (1973), 1520.CrossRefGoogle Scholar
(2)Beineke, L. W. and Fiorini, S. On a conjecture on graphs critical with respect to edge colouring (to appear).Google Scholar
(3)Fiorini, S. and Wilson, R. J. On the chromatic index of a graph, II, Combinatorias. Proceedings of the British Combinatorial Conference, Aberystwyth (1973) (to appear).CrossRefGoogle Scholar
(4)Harary, F.Graph Theory. Addison-Wesley (Reading, Mass., 1969).CrossRefGoogle Scholar
(5)Jakobsen, I. T.Some remarks on the chromatic index of a graph. Arch. Math. (Basel) 24 (1973), 440448.CrossRefGoogle Scholar
(6)Vizing, V. G.On an estimate of the chromatic class of a p-graph (Russian). Diskret. Analiz 3 (1964), 2530.Google Scholar
(7)Vizing, V. G.The chromatic class of a multigraph. Cybernetics 1 No. 3 (1965), 3241.CrossRefGoogle Scholar
(8)Vizing, V. G.Critical graphs with a given chromatic class (Russian). Diskret. Analiz 5 (1965), 917.Google Scholar
(9)Vizing, V. G.Some unsolved problems in graph theory. Russian Math. Surveys 23 (1968), 125141.CrossRefGoogle Scholar