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Ore and Erdős type conditions for long cycles in balanced bipartite graphs

Abstract : We conjecture Ore and Erdős type criteria for a balanced bipartite graph of order 2n to contain a long cycle C(2n-2k), where 0 <= k < n/2. For k = 0, these are the classical hamiltonicity criteria of Moon and Moser. The main two results of the paper assert that our conjectures hold for k = 1 as well.
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Janusz Adamus, Lech Adamus. Ore and Erdős type conditions for long cycles in balanced bipartite graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2009, Vol. 11 no. 2 (2), pp.57--69. ⟨10.46298/dmtcs.459⟩. ⟨hal-00988209⟩

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