The asymptotic spectrum of graphs and the Shannon capacity

Abstract

We introduce the asymptotic spectrum of graphs and apply the theory of asymptotic spectra of Strassen (J. Reine Angew. Math. 1988) to obtain a new dual characterisation of the Shannon capacity of graphs. Elements in the asymptotic spectrum of graphs include the Lov\'asz theta number, the fractional clique cover number, the complement of the fractional orthogonal rank and the fractional Haemers bounds.