Regular homogeneously traceable nonhamiltonian graphs

A graph is called homogeneously traceable if every vertex an endpoint of a Hamilton path. In 1979 Chartrand, Gould and Kapoor proved that for integer n≥9, there exists nonhamiltonian order n. The graphs they constructed are irregular. Thus it natural to consider the existence problem regular graphs. We prove two results: (1) For even n≥10, cubic n; (2) p≥18, 4-regular p circumference p−4. Unsolved problems posed.