Hamilton-Connected Mycielski Graphs∗

Abstract

Jarnicki, Myrvold, Saltzman, and Wagon conjectured that if G is Hamilton-connected and not K2, then its Mycielski graph μG is Hamilton-connected. In this paper, we confirm that the conjecture is true for three families of graphs: the graphs G with δG>VG/2, generalized Petersen graphs GPn,2 and GPn,3, and the cubes G3. In addition, if G is pancyclic, then μG is pancyclic.