On the Shannon capacity of sums and products of graphs
Abstract
Let (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 (G H)>(G)+(H) and (G H)>(G)(H). This was shown independently by Wigderson and Zuiddam [2022] using Kadison-Dubois duality and the Axiom of choice.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.