An Ore-Type Condition for Hamiltonicity in Tough Graphs and the Extremal Examples
Masahiro Sanka,
Songling Shan
Abstract:Let $G$ be a $t$-tough graph on $n\ge 3$ vertices for some $t>0$. It was shown by Bauer et al. in 1995 that if the minimum degree of $G$ is greater than $\frac{n}{t+1}-1$, then $G$ is hamiltonian. In terms of Ore-type hamiltonicity conditions, the problem was only studied when $t$ is between 1 and 2, and recently the second author proved a general result. The result states that if the degree sum of any two nonadjacent vertices of $G$ is greater than $\frac{2n}{t+1}+t-2$, then $G$ is hamiltonian. It was conj… Show more
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