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Chromatic Number and Topological Complete Subgraphs

Published online by Cambridge University Press:  20 November 2018

G. A. Dirac
G. A. Dirac*
Affiliation:
University of Dublin, Eire
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A graph with m(>1) vertices, each pair of distinct vertices connected by an edge, and also a graph obtained from such a graph by the process of subdividing edges through the insertion of new vertices of valency 2, will be denoted by ≪m, o≫. A graph obtained from a graph with m(>2) vertices in which each pair of distinct vertices are connected by an edge, by deleting n (≤ m-1) edges incident with one and the same vertex, and also a graph obtained from such a graph by the process of subdividing edges through the insertion of new vertices of valency 2, will be denoted by ≪m, n≫.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 6 , December 1965 , pp. 711 - 715
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Dirac, G. A., A property of 4-chromatic graphs and some remarks on critical graphs. Journal London Math. Soc. 27 (1952), 87. Bernhardine ZeidI, Űber 4- und 5-chrome Graphen, Monatsh. Math.62 (1958), 212.Google Scholar
2. Dirac, G. A., In abstrakten Graphen vorhandene vollstandige 4- Graphen und ihre Unterteilungen, Math. Nachrichten, 22 (1960), 61.Google Scholar
3. Wagner, K., Beweis einer Abschwächung der Hadwiger Vermutung, Math. Annalen 153 (1964), 139.Google Scholar