Work

On Vizing’s Problem for Triangle-Free Graphs

Year: 2025

Type: article

Abstract: 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.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/12703

Authors: Ross J. Kang, Matthieu Rosenfeld

Institutions: University of Amsterdam, Centre National de la Recherche Scientifique, Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Awards: G565383568, On the edge: theory and techniques at the frontiers of edge-colouring