Cycles Through Specified Vertices in $1$-Tough Graphs

Abstract

Bollobás, Brightwell [1] and independently Shi [3] proved the existence of a cycle through all vertices of degree at least $\frac{n}{2}$ in any $2$-connected graph of order $n$. The aim of this paper is to show that the above degree requirement can be relaxed for $1$-tough graphs.