Independent dominating sets and hamiltonian cycles |
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| Authors: | Penny Haxell Ben Seamone Jacques Verstraete |
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| Affiliation: | Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Ontario N2L 3G1 Canada |
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| Abstract: | A graph is uniquely hamiltonian if it contains exactly one hamiltonian cycle. In this note we prove that there are no r‐regular uniquely hamiltonian graphs when r > 22. This improves upon earlier results of Thomassen. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 233–244, 2007 |
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| Keywords: | independent dominating set hamiltonian cycle regular graphs uniquely hamiltonian |
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