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Spectral radius and the 2-power of Hamilton paths

Te Pi, Rui Sun, Long-Tu Yuan

Abstract

We determine the maximum number of a graph without containing the 2-power of a Hamilton path. Using this result, we establish a spectral condition for a graph containing the 2-power of a Hamilton path.

Spectral radius and the 2-power of Hamilton paths

Abstract

We determine the maximum number of a graph without containing the 2-power of a Hamilton path. Using this result, we establish a spectral condition for a graph containing the 2-power of a Hamilton path.
Paper Structure (3 sections, 8 theorems, 2 equations, 1 table)

This paper contains 3 sections, 8 theorems, 2 equations, 1 table.

Table of Contents

  1. Introduction
  2. Proof of Theorem \ref{['theorem1.1']}
  3. Proof of Theorem \ref{['theorem2']}

Key Result

Theorem 1.1

Let $G$ be a graph on $n\geqslant4$ vertices. If $e(G)\geqslant {n-1 \choose 2}+1$, then $G$ contains a Hamilton cycle unless $G= K_n -E(S_{n-1})$ or $G=K_5 -E(K_3)$.

Theorems & Definitions (8)

  • Theorem 1.1: Ore 1961Ore315
  • Theorem 1.2
  • Corollary 1.3
  • Theorem 1.4: Yan, He, Feng and Liu 2023Yan113155
  • Theorem 1.5
  • Proposition 2.1
  • Lemma 3.1: Fiedler and Nikiforov 2010Fiedler2170
  • Lemma 3.2: Hong 1988Yuan135