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).
Journal of Combinatorial Theory. Series B
Balister, P., Bollobás, B., Riordan, O., & Schelp, R. (2003). Graphs with large maximum degree containing no odd cycles of a given length. Journal of Combinatorial Theory. Series B, 87 (2), 366-373. https://doi.org/10.1016/S0095-8956(02)00024-2