Work

Hoffman colorability of (strongly) regular graphs

Year: 2025

Type: article

Abstract: Hoffman's bound is a well-known eigenvalue bound on the chromatic number of a graph. By interpreting this bound as a parameter, we show multiple applications of colorings attaining the bound (Hoffman colorings) for several notions of graph regularity: regular, (co-)edge-regular, and strongly regular. For strongly regular graphs, we prove that Hoffman colorability implies pseudo-geometricity, and we strengthen Haemers' finiteness result on strongly regular graphs with a bounded chromatic number by considering the Hoffman bound instead of the chromatic number. Furthermore, by using Hoffman colorings we show that a sufficient condition for non-unique vector colorability shown by Godsil, Roberson, Rooney, Šámal and Varvitsiotis [European J. Combin. 79, 2019] can be relaxed in the setting of strongly regular graphs. Lastly, using Hoffman colorings we derive several new characterizations of the mentioned graph regularity notions.

Source: Discrete Mathematics

DOI: 10.1016/j.disc.2025.114856

Authors: Aida Abiad, Bart De Bruyn, Thijs van Veluw

Institutions: Vrije Universiteit Brussel, Eindhoven University of Technology, Ghent University

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,320

Funders: Nederlandse Organisatie voor Wetenschappelijk Onderzoek, Universiteit Gent, Bijzonder Onderzoeksfonds UGent