A Sufficient Condition for Edge Chromatic Critical Graphs to Be Hamiltonian—An Approach to Vizing's 2‐Factor Conjecture |
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| Authors: | Rong Luo Yue Zhao |
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| Institution: | 1. DEPARTMENT OF MATHEMATICS WEST VIRGINIA UNIVERSITY MORGANTOWN, , 26506‐6310 WEST VIRGINIA;2. DEPARTMENT OF MATHEMATICS UNIVERSITY OF CENTRAL FLORIDA ORLANDO, , 32816‐1364 FLORIDA |
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| 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 |
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| Keywords: | edge colorings critical graphs 2‐factors Hamiltonian cycles |
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