The chromatic index of strongly regular graphs

TL;DR

This paper investigates the edge-coloring properties of strongly regular graphs, determining their chromatic index for many cases and proposing a conjecture that most are class 1, with some results supported by computational searches.

Contribution

It provides new results on the chromatic index of strongly regular graphs, including computational determinations and a conjecture about their class 1 status for even order graphs.

Findings

Most investigated SRGs of even order are class 1.

The chromatic index equals the degree for many SRGs.

A conjecture that all connected even order SRGs are class 1.

Abstract

We determine (partly by computer search) the chromatic index (edge-chromatic number) of many strongly regular graphs (SRGs), including the SRGs of degree $k \leq 18$ and their complements, the Latin square graphs and their complements, and the triangular graphs and their complements. Moreover, using a recent result of Ferber and Jain it is shown that an SRG of even order $n$, which is not the block graph of a Steiner 2-design or its complement, has chromatic index $k$, when $n$ is big enough. Except for the Petersen graph, all investigated connected SRGs of even order have chromatic index equal to their degree, i.e., they are class 1, and we conjecture that this is the case for all connected SRGs of even order.