Relaxations of Ore's Condition on Cycles

A simple, undirected 2-connected graph G of order n belongs to class O(n,), 0, if 2 = n - . It is well known (Ore's theorem) that G is hamiltonian if = 0, in which case the 2-connectedness hypothesis is implied. In this paper we provide a method for studying this class of graphs. As an application we give a full characterization of graphs G in O(n,), 3, in terms of their dual hamiltonian closure.

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Ahmed Ainouche
• Keywords: 2-connectedness Hypothesis, COMBINATORICS 2006, Dual Hamiltonian Closure, Undirected