【摘要】 分别以Ｘ（Ｇ）、Ｘ１（Ｇ）、Ｘ２（Ｇ）记图Ｇ之色数、边色数和金色数，对任意Ｐ阶图Ｇ及其补图，当Ｘ１（Ｇ）、Ｘ１（Ｇ）不为零时，本文得到下面三个Ｎｏｒｄｈａｕｓ－Ｇａｄｄｕｍ型乘积的下界：对于每一工整数Ｐ，这三个下界均可达到。更多还原

【Abstract】 Let the chromatic number of G, the edge chromatic number of G and the total chromatic of G be denoted by X(G)9 X1(G) and X2(G), respectivery.We obtain the lowser bounds of three products of the Nordhaus-Gaddum class as follows:where we assume that neither X1 (G) nor X1 (G) is equal to zero. All these bounds are sharp for every positive integer p.更多还原