A spectral condition for odd cycles in graphs

TL;DR

This paper establishes a precise spectral criterion to determine when a graph contains odd cycles, providing a new tool for analyzing graph structure based on eigenvalues.

Contribution

It introduces a sharp spectral condition for odd cycle existence and proves a related stability result, advancing spectral graph theory.

Findings

Spectral condition guarantees odd cycles in graphs

Proved a stability result related to spectral conditions

Enhanced understanding of graph structure via eigenvalues

Abstract

We give a sharp spectral condition for the existence of odd cycles in a graph of given order. We also prove a related stability result.