Graphs with large maximum degree containing no odd cycles of a given length


Let us write f(n, Δ; C2k+1) for the maximal number of edges in a graph of order n and maximum degree Δ that contains no cycles of length 2k + 1. For n/2 ≤ Δ ≤ ?n - k - 1 and n sufficiently large we show that f(n,Δ; C2k+1) = Δ(n - Δ), with the unique extremal graph a complete bipartite graph. © 2002 Published by Elsevier Science (USA).

Publication Title

Journal of Combinatorial Theory. Series B