Coloring edges of self-complementary graphs (Q1373172)

According to the well-known Vizing theorem a graph \(G\) is said to be Class 1 (Class 2) if the chromatic index of \(G\) equals \(h (h+1)\), where \(h\) is the maximum vertex degree of \(G\). The authors show: (i) if a self-complementary graph \(G\) has a complementing permutation that is a cycle, then \(G\) is Class 1, and (ii) every regular self-complementary graph is Class 2. The authors conjecture that a self-complementary graph is Class 2 iff it is regular.