Hamilton-Connected Mycielski Graphs∗.

Jarnicki, Myrvold, Saltzman, and Wagon conjectured that if G is Hamilton-connected and not K 2 , then its Mycielski graph μ G is Hamilton-connected. In this paper, we confirm that the conjecture is true for three families of graphs: the graphs G with δ G > V G / 2 , generalized Petersen graphs G P n , 2 and G P n , 3 , and the cubes G 3 . In addition, if G is pancyclic, then μ G is pancyclic. [ABSTRACT FROM AUTHOR]