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 \(k \geq 3\), or \(G\) is vertex pancyclic for \(k = 2\). This result improves a result of Broersma, Xiong, and Yoshimoto.