Cycle Lengths in Hamiltonian Graphs with a Pair of Vertices Having Large Degree Sum

A graph of order n is said to be pancyclic if it contains cycles of all lengths from three to n. Let G be a hamiltonian graph and let x and y be vertices of G that are consecutive on some hamiltonian cycle in G. Hakimi and Schmeichel showed [2] that if d(x)+d(y) n then either G is pancyclic, G has cycles of all lengths except n - 1 or G is isomorphic to a complete bipartite graph. In this paper, we study the existence of cycles of various lengths in a hamiltonian graph G given the existence of a pair of vertices that have a high degree sum but are not adjacent on any hamiltonian cycle in G. Keywords hamiltonian cycle

• Type: Journal
• Year: 2010
• Where: GC
• Authors: Michael Ferrara, Michael S. Jacobson, Angela Harris
• Keywords: Applied Computing, GC 2010, Hamiltonian Cycle, Hamiltonian Graph, Keywords Hamiltonian Cycle