On the chromatic number of graphs with some restriction of vertex degrees - S.N. Selezneva (Учёные записки Казанского университета: Серия Физико-математические науки)
Graphs, for which the degree of a certain vertex is equal to (d + 1) and the degrees of all other vertices are at most d , d ≥ 3 , were considered. Properties were obtained to color vertices of these graphs in d colors.