Hamilton-Connected Mycielski Graphs∗

Abstract

Jarnicki, Myrvold, Saltzman, and Wagon conjectured that if $G$ is Hamilton-connected and not $K_2$ , then its Mycielski graph $\mu \left(G\right)$ is Hamilton-connected. In this paper, we confirm that the conjecture is true for three families of graphs: the graphs $G$ with $\delta \left(G\right)>\left|V\left(G\right)\right|/2$ , generalized Petersen graphs $GP\left(n,2\right)$ and $GP\left(n,3\right)$ , and the cubes $G^3$ . In addition, if $G$ is pancyclic, then $\mu \left(G\right)$ is pancyclic.