A Sufficient Condition for Edge Chromatic Critical Graphs to Be Hamiltonian—An Approach to Vizing's 2‐Factor Conjecture. Issue 4 (11th July 2012) - Luo, Rong; Zhao, Yue
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 <inline-graphic mimetype="image" xlink:href="ark:/27927/pgg21g219bd" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />Δ≥6n7, 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<inline-graphic mimetype="image" xlink:href="ark:/27927/pgg21g21989" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />2Δ, n.© 2012 Wiley Periodicals, Inc. J. Graph Theory 00: 1‐14, 2012