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Edge Maximal Non-Bipartite Graphs Without Odd Cycles of Prescribed Lengths

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Abstract.

 Let ?(n;3,5,…,2k+1) denote the class of non-bipartite graphs on n vertices having no odd cycle of length ≤2k+1. We prove that for every G∈?(n;3,5,…,2k+1) and characterize the extremal graphs. We also study the subclass ℋ(n;3,5,…,2k+1) consisting of the hamiltonian members of ?(n;3,5,…, 2k+1). For this subclass the above upper bound holds for odd n. For even n we establish the following sharp upper bound:

and characterize the extremal graphs.

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Received: February 28, 1997 Final version received: August 31, 2000

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Caccetta, L., Jia, RZ. Edge Maximal Non-Bipartite Graphs Without Odd Cycles of Prescribed Lengths. Graphs Comb 18, 75–92 (2002). https://doi.org/10.1007/s003730200004

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  • DOI: https://doi.org/10.1007/s003730200004

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