The Clique Number and Some Hamiltonian Properties of Graphs

Abstract

Abstract A graph is said to be Hamiltonian (respectively, traceable) if it has a Hamiltonian cycle (respectively, Hamiltonian path), where a Hamiltonian cycle (respectively, Hamiltonian path) is a cycle (respectively, path) containing all the vertices of the graph. In this short note, sufficient conditions involving the clique number for the Hamiltonian and traceable graphs are presented.