Hamilton and long cycles in $t$-tough graphs with $t>1$

Abstract

It is proved that if $G$ is a $t$-tough graph of order $n$ and minimum degree $\delta$ with $t>1$ then either $G$ has a cycle of length at least $\min \{n,2\delta +4\}$ or $G$ is the Petersen graph.

arXiv comment19 pages. arXiv admin note: text overlap with arXiv:1201.1551 and arXiv:1201.6330