The chromatic index of strongly regular graphs - Cioaba, Sebastian M. (Ars mathematica contemporanea, 2021)
We determine (partly by computer search) the chromatic index (edge-chromatic number) of many strongly regular graphs (SRGs), including the SRGs of degree ?$k ≤ 18$? 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, we prove 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 ?$k$?, i.e., they are class 1, and we conjecture that this is the case for all connected SRGs of even order.
Keywords: 1-factorization; 1-faktorizacija; barvanje povezav; chromatic index; edge coloring; krepko regularen graf; kromatični indeks; strongly regular graph