A graph G is hamiltonian-connected if any two of its vertices are connected by a Hamilton path (a path including every vertex of G); and G is s-hamiltonian-connected if the deleti...
For each integer m 1, consider the graph Gm whose vertex set is the set N = {0, 1, 2, . . . } of natural numbers and whose edges are the pairs xy with y = x + m or y = x - m or y...