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On the Shannon capacity of sums and products of graphs
Published 14 Apr 2022 in math.CO | (2204.06853v1)
Abstract: Let $\Theta(G)$ denote the Shannon capacity of a graph $G$. We give an elementary proof of the equivalence, for any graphs $G$ and $H$, of the inequalities $\Theta(G\sqcup H)>\Theta(G)+\Theta(H)$ and $\Theta(G\boxtimes H)>\Theta(G)\Theta(H)$. This was shown independently by Wigderson and Zuiddam [2022] using Kadison-Dubois duality and the Axiom of choice.
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