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Graphs without cycles of even length

Published online by Cambridge University Press:  17 April 2009

Thomas Lam
Thomas Lam
Affiliation:
School of Mathematics, The University of New South Wales, Sydney NSW 2052, Australia
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Abstract

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Dedicated to George Szekeres on his ninetieth birthday

In this paper we prove that a bipartite graph with parts of sizes M and N, having no cycles of even length less that or equal to 2(2k + 1), where k is a positive integer, has at most (NM)(k+1)/(2k+1) + Dk(N + M) edges, where Dk only depends on k.

In particular, we show that when k = 1, D1 = 1 is possible.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 3 , June 2001 , pp. 435 - 440
Copyright
Copyright © Australian Mathematical Society 2001

References

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