Abstract
A Nordhaus-Gaddum theorem states bounds on p(G)+p(G‾) and p(G)⋅p(G‾) for some graph parameter p(G). We consider the sum upper bound for degeneracy, chromatic number, fractional and circular chromatic number, list chromatic number, span (for L(2,1) labeling), and point partition number. Viewing {G,G‾} as a decomposition of Kn, we describe a strategy to determine the extremal decompositions for these parameters. This produces short proofs of several existing results as well as several new theorems.
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