Beineke, L. W. and Chartrand, G. "The Coarseness of a Graph." Compos. Math.19, 290-298, 1968.Beineke, L. W. and Guy, R. K. "The Coarseness of the Complete Bipartite Graph." Canad. J. Math.21, 1086-1096, 1969.Guy, R. and Beineke, L. "'THe Coarseness of the Complete Graph." Canad. J. Math.20, 888-894, 1968.Harary, F. "Covering and Packing in Graphs, I." Ann. New York Acad. Sci.175, 198-205, 1970.Harary, F. Graph Theory. Reading, MA: Addison-Wesley, pp. 121-122, 1994.Harary, F. and Palmer, E. M. Graphical Enumeration. New York: Academic Press, p. 225, 1973.Harary, F. and Palmer, E. M. "A Survey of Graph Enumeration Problems." In A Survey of Combinatorial Theory (Ed. J. N. Srivastava). Amsterdam: North-Holland, pp. 259-275, 1973.Kainen, P. C. "Thickness and Coarseness of Graphs." Abh. Math. Semin. Univ. Hamburg39, 88-95, 1973.
的粗糙度 
是给定图 
中包含的最大数量的边不相交的非平面子图。因此，平面图 
的粗糙度为 
。
的粗糙度对于 
的大多数值是已知的，除了 
、
可被 3 整除且大于或等于 18，以及 
形式为 
的情况。对于所有这些情况，已知值在 1 以内 (Guy and Beineke 1968; Harary 1994, pp. 121-122)。
的粗糙度对于满足某些条件的 
值是已知的 (Beineke and Guy 1969; Harary 1994, pp. 121-122)。