A Sufficient Condition for Edge Chromatic Critical Graphs to Be Hamiltonian—An Approach to Vizing's 2-Factor Conjecture


  • Contract grant sponsor: NSF-China; Contract grant number: NSFC 11171228 (to R. L.); Contract grant sponsor: National Security Agency; Contract grant numbers: H98230-06-1-0085; H98230-10-1-0169 (to Y. Z.).


In this article, we consider Vizing's 2-Factor Conjecture which claims that any Δ-critical graph has a 2-factor, and show that if G is a Δ-critical graph with n vertices satisfying math formula, then G is Hamiltonian and thus G has a 2-factor. Meanwhile in this article, we also consider long cycles of overfull critical graphs and obtain that if G is an overfull Δ-critical graph with n vertices, then the circumference of G is at least minmath formula.© 2012 Wiley Periodicals, Inc. J. Graph Theory 00: 1-14, 2012