A Sufficient Condition for Edge Chromatic Critical Graphs to Be Hamiltonian—An Approach to Vizing's 2‐Factor Conjecture
Rong Luo, Yue Zhao · Journal of Graph Theory · 2012
Abstract 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 , 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 min .© 2012 Wiley Periodicals, Inc. J. Graph Theory 00: 1‐14, 2012