Abstract
In this paper, maximal non-Hamiltonian graphs ( MNH graphs), i.e., non-Hamiltonian graphs such that the addition of any new edge violates their property of being non-Hamiltonian are studied. It is shown that the study of MNH graphs can be reduced to the study of the so-called simplified MNH graphs. Restrictions on the structure of maximal cliques of simplified MNH graphs are obtained, the orders and the number of such graphs are estimated.
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Roldugin, P.V. On the Number of Non-Hamiltonian Graphs. Mathematical Notes 75, 652–659 (2004). https://doi.org/10.1023/B:MATN.0000030973.71346.2f
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DOI: https://doi.org/10.1023/B:MATN.0000030973.71346.2f