An Erd\H{o}s-Stone type result for high-order spectra of graphs

Abstract

Erd\H{o}s-Stone Theorem is a well-known result in extremal graph theory which determines the asymptotic behaviour of maximum number of edges in an $n$-vertex $H$-free graph. In 2009, Nikiforov gave a spectral version of Erd\H{o}s-Stone Theorem. In this paper, we obtain a tensor's spectral version of Erd\H{o}s-Stone Theorem.