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A Sufficient Condition for Edge Chromatic Critical Graphs to Be Hamiltonian—An Approach to Vizing's 2‐Factor Conjecture
Author(s) -
Luo Rong,
Zhao Yue
Publication year - 2013
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.21689
Subject(s) - mathematics , combinatorics , critical graph , conjecture , edge coloring , hamiltonian path , graph , discrete mathematics , chromatic scale , hamiltonian (control theory) , foster graph , graph theory , graph power , line graph , mathematical optimization
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 Δ ≥ 6 n 7 , 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 { 2 Δ , n } .© 2012 Wiley Periodicals, Inc. J. Graph Theory 00: 1‐14, 2012