Chvátal-Erdős condition for 2-factors with at most two components in graphs
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It is well-known that Chvátal and Erdős stated that any graph of order at least three whose independence number is no greater than its connectivity is Hamiltonian; that any graph whose independence number is no greater than its connectivity minus one is Hamilton-connected; and that any graph whose independence number is no greater than its connectivity plus one is traceable. Kaneko and Yoshimoto [J. Graph Theory 43 (2003) 269--279] showed that every 4-connected graph of order at least six has a 2-factor with two components if its independence number is no greater than its connectivity. In this paper, we show that any connected graph of order at least three times its connectivity plus three has a 2-factor with at most two components, except for one exceptional class, if its independence number is no greater than its connectivity plus one. Our result is best possible.
Fields of Study & Subjects
Advanced Graph Theory Research
Limits and Structures in Graph Theory
Graph theory and applications
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 13 March 2026
- Language
- EN
- Document type
- Preprint