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Graphs without cycles of even length
Published online by Cambridge University Press: 17 April 2009
Abstract
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.
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- Copyright © Australian Mathematical Society 2001
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