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Matematicheskie Zametki, 2004, Volume 75, Issue 5, Pages 702–710
DOI: https://doi.org/10.4213/mzm66 (Mi mzm66) 		 
On the Number of Non-Hamiltonian Graphs

P. V. Roldugin

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
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DOI: https://doi.org/10.4213/mzm66
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.
Received: 06.02.2003
Revised: 18.04.2003
English version:
Mathematical Notes, 2004, Volume 75, Issue 5, Pages 652–659
DOI: https://doi.org/10.1023/B:MATN.0000030973.71346.2f
Bibliographic databases:
UDC: 519.1
Language: Russian
Citation: P. V. Roldugin, “On the Number of Non-Hamiltonian Graphs”, Mat. Zametki, 75:5 (2004), 702–710; Math. Notes, 75:5 (2004), 652–659
Citation in format AMSBIB
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