On Vizing’s Problem for Triangle-Free Graphs
We prove that $\chi(G) \le \lceil (\Delta+1)/2\rceil+1$ for any triangle-free graph $G$ of maximum degree $\Delta$ provided $\Delta \ge 524$. This gives tangible progress towards an old problem of Vizing, in a form cast by Reed. We use a method of Hurley and Pirot, which in turn relies on a new counting argument of the second author.
Authors
- Ross J. Kang (ORCID: https://orcid.org/0000-0002-4219-593X)
- Matthieu Rosenfeld (ORCID: https://orcid.org/0000-0001-5467-5407)
Publication Details
- Journal
- The Electronic Journal of Combinatorics
- Published
- 2025-10-03
- DOI
- https://doi.org/10.37236/12703
- Primary Topic
- Limits and Structures in Graph Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek