ON HOMOGENEOUSLY TRACEABLE NONHAMILTONIAN GRAPHS

Abstract

SummaryA graph G is homogeneously traceable if for every vertex v of G there exists a hamiltonian path with initial vertex v. It is shown that there exists a homogeneously traceable nonhamiltonian graph of order p, for all positive integers p except for 3 ≤p≤ 8. Further, if G is a homogeneously traceable nonhamiltonian graph of order p, then {5p/4} is a sharp lower bound on the size of G and the maximum degree of G is at most p– 4 for p≥ 9.