The chromatic index of strongly regular graphs

Sebastian M. Cioabă, Krystal Guo, Willem H. Haemers

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 ≤ 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


Strongly regular graph, chromatic index, edge coloring, 1-factorization

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DOI: https://doi.org/10.26493/1855-3974.2435.ec9

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications