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On the structure of k-chromatic graphs

Published online by Cambridge University Press:  24 October 2008

G. A. Dirac
G. A. Dirac
Affiliation:
Aaarhus Universitet, Denmark
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Abstract

It is shown that for k ≥ 5 in every k-chromatic graph there is a set of k distinct vertices V1, …, Vk with the property that for i, j = 1, …, k and i ≠ j the graph contains the union of a set of 4 paths connecting Vi and Vj no two of which have any edge or any vertex besides Vi and Vj in common and k − 1 paths connecting Vi and Vj no two of which have any edge in common.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 3 , July 1967 , pp. 683 - 691
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

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