Mathematics and Statistics
AKCE International Journal of Graphs and Combinatorics
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 (Formula presented.) Chvátal’s sufficient condition is also necessary. In contrast, we essentially prove that for every (Formula presented.), the sufficient condition of Bondy and Boesch for forcible k-connectedness is not necessary in the same way.
Degree condition, forcibly Hamiltonian degree sequence, forcibly k-connected degree sequence
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Douglas Bauer, Linda Lesniak, Aori Nevo, and Edward Schmeichel. "On the necessity of Chvátal’s Hamiltonian degree condition" AKCE International Journal of Graphs and Combinatorics (2020): 665-669. https://doi.org/10.1080/09728600.2020.1834337