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

Luo Rong | Zendy; Zhao Yue | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

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

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research