A survey of Nordhaus–Gaddum type relations

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Abstract

In 1956, Nordhaus and Gaddum gave lower and upper bounds on the sum and the product of the chromatic number of a graph and its complement, in terms of the order of the graph. Since then, relations of a similar type have been proposed for many other graph invariants, in several hundred papers. We present a survey on this research endeavor.

Keywords

Nordhaus–Gaddum
Graph
Complement
Inequalities
Invariants

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