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An Erdős-Stone type result for high-order spectra of graphs

Chunmeng Liu, Jiang Zhou, Changjiang Bu

Abstract

Erdős-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 Erdős-Stone Theorem. In this paper, we obtain a tensor's spectral version of Erdős-Stone Theorem.

An Erdős-Stone type result for high-order spectra of graphs

Abstract

Erdős-Stone Theorem is a well-known result in extremal graph theory which determines the asymptotic behaviour of maximum number of edges in an -vertex -free graph. In 2009, Nikiforov gave a spectral version of Erdős-Stone Theorem. In this paper, we obtain a tensor's spectral version of Erdős-Stone Theorem.
Paper Structure (3 sections, 11 theorems, 34 equations)

This paper contains 3 sections, 11 theorems, 34 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proofs of theorems

Key Result

Theorem 1.1

Stone Let $H$ be a graph with chromatic number $\chi(H)=r+1$. For an arbitrary positive number $\epsilon$, there is a positive number $n_{0}(\epsilon, H)$ such that for $n > n_{0}(\epsilon, H)$,

Theorems & Definitions (16)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Remark 1
  • Definition 1.4
  • Theorem 1.5
  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Lemma 2.4
  • ...and 6 more