On the chromatic index of cographs and join graphs

Along with a result of Niessen of 1994, a conjecture proposed by Hilton and Chetwynd of 1986 implies that the chromatic index of graphs with Δ≥n/2 can be determined in linear time. Connected cographs satisfy Δ≥n/2, however whether the conjecture holds for cographs is still unknown. This paper presents sufficient conditions for cographs and join graphs to be Class 1.