Panconnectedness of $K$-trees with Sufficiently Large Toughness

Abstract

In this paper, we prove that if the toughness of a $k$-tree $G$ is at least $\frac{k+1}{3}$, then $G$ is panconnected for $k\ge 3$, or $G$ is vertex pancyclic for $k=2$. This result improves a result of Broersma, Xiong, and Yoshimoto.