The edge-chromatic class of regular graphs of degree 4 and their complements (Q1087882)

When scheduling round robin tournaments, how many rounds may be selected at random so as to be able still to complete the total schedule? In this paper it is shown that 4 rounds may always be drawn, except for one special case with 6 players. The problem is treated as the existence of a 1-factorization for the complement of a regular graph of even order, in other words that there exists an edge-colouring with no more colours than the degree of the (regular) graph, i.e. the graph is of class 1. As part of the proof a list is obtained of all 8 regular graphs of order at most 10 which are not of class 1.