On degree conditions of semi-balanced k-partite Hamiltonian graphs

Abstract

For two integers [Formula: see text] and [Formula: see text] with [Formula: see text], a [Formula: see text]-partite graph is said to be a semi-balanced[Formula: see text]-partite graph if each partite set has either [Formula: see text] or [Formula: see text] vertices. We give some degree conditions for semi-balanced [Formula: see text]-partite graphs to be Hamiltonian and almost pancyclic, respectively. Furthermore, using these results, we obtain the degree conditions for a balanced [Formula: see text]-partite graph to be vertex bipancyclic if [Formula: see text] is even, and vertex [Formula: see text]-pancyclic if [Formula: see text] is odd.