Four sufficient conditions for hamiltonian graphs

Abstract

The purpose of this communication is to describe four new sufficient conditions for the existence of hamiltonian circuits in graphs. We mention first ten known results. Each one can be derived from at least one of the new conditions. We consider only undirected graphs G=( V, E) without loops. We assume that G is k-connected. For S ⊂ N, we denote by N( S) the set of vertices adjacent to at least one vertex of S and by d( S) the cardinality of this set.