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On certain cycles in graphs

Published online by Cambridge University Press:  20 January 2009

Douglas D. Grant
Douglas D. Grant
Affiliation:
Napier CollegeEdinburgh
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We show that every simple graph of order 2r and minimum degree ≧4r/3 has the property that for any partition of its vertex set into 2-subsets, there is a cycle which contains exactly one vertex from each 2-subset. We show that the bound 4r/3 cannot be lowered to r, but conjecture that it can be lowered to r + 1.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 24 , Issue 1 , February 1981 , pp. 15 - 17
Copyright
Copyright © Edinburgh Mathematical Society 1981

References

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