Class 1 conditions depending on the minimum degree and the number of vertices of maximum degree
Thomas E.W Nießen, Lutz Volkmann · Journal of Graph Theory · 1990
Abstract A graph is called Class 1 if the chromatic index equals the maximum degree. We prove sufficient conditions for simple graphs to be Class 1. Using these conditions we improve results on some edge‐coloring theorems of Chetwynd and Hilton. We also improve a theorem concerning the 1‐factorization of regular graphs of high degree.