Hamilton cycles in vertex-transitive graphs of order $6p$

Abstract

It was shown by Kutnar and \v Sparl in 2009 that every connected vertex-transitive graph of order $6p$, where $p$ is a prime, contains a Hamilton path. In this paper, it will be shown that every such graph contains a Hamilton cycle, except for the triangle-replaced graph of the Petersen graph.

Figures (2)

• Figure 1: The quotient graph $X_{\mathcal{S}}$ with respect to the $(6,p)$-semiregular automorphism $\rho=s(0,1)$ when $\beta^{t^i\ell H}\subset N_1(\alpha)$.
• Figure 2: The quotient graph $X_{\mathcal{S}}$ with respect to the $(6,p)$-semiregular automorphism $\rho=s(0,1)$ when $\alpha^{t^j\ell H}\cup\beta^{t^{i}H}\subset N_1(\alpha)$.

Theorems & Definitions (32)

• Theorem 1.1
• Proposition 2.1
• Proposition 2.2
• Proposition 2.3
• Proposition 2.4
• Proposition 2.5
• Proposition 2.6
• Lemma 2.7
• Proposition 2.8
• Proposition 2.9