Cioabă–Guo–Haemers conjecture on the chromatic index of connected strongly regular graphs

A strongly regular graph (SRG) $G$ with parameters $(n,k,\lambda,\mu)$ is a $k$-regular graph on $n$ vertices such that every adjacent pair has exactly $\lambda$ common neighbors and every distinct non-adjacent pair has exactly $\mu$ common neighbors. A graph is class 1 when its chromatic index equals its degree; a graph has even order when its number of vertices $n$ is even. Cioabă–Guo–Haemers' conjecture. Except for the Petersen graph, every connected SRG of even order is class 1. The claim is motivated by computations and asymptotic results showing class 1 behavior for broad families of connected SRGs, but the general case remains open; the Petersen graph is the known exception, with edge-chromatic number $4$ rather than $3$.