On the necessity of Chvátal’s Hamiltonian degree condition
Douglas Bauer, Linda Lesniak, Aori Nevo and 1 more
AKCE International Journal of Graphs and Combinatorics · 2020
doi:10.1080/09728600.2020.1834337 (opens in a new tab)
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Abstract
In 1972 Chvátal gave a well-known sufficient condition for a graphical sequence to be forcibly Hamiltonian, and showed that in some sense his condition is best possible. In this paper, we conjecture that with probability 1 as Chvátal’s sufficient condition is also necessary. In contrast, we essentially prove that for every, the sufficient condition of Bondy and Boesch for forcible k-connectedness is not necessary in the same way.
Abstract licence: CC BY-NC
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