Extremal graphs in some coloring problems.

Department of Mathematics, Annamalai University, Annamalainagar 608 002, India
Discrete Mathematics (Impact Factor: 0.57). 05/1998; 186:15-24. DOI: 10.1016/S0012-365X(97)00216-1
Source: DBLP

ABSTRACT For a simple graph G with chromatic number χ(G), the Nordhaus-Gaddum inequalities give upper and lower bounds for χ(G)χ(Gc) and χ(G) + χ(Gc). Based on a characterization by Fink of the extremal graphs G attaining the lower bounds for the product and sum, we characterize the extremal graphs G for which A(G)B(Gc) is minimum, where A and B are each of chromatic number, achromatic number and pseudoachromatic number. Characterizations are also provided for several cases in which A(G) + B(Gc) is minimum.