Spectral conditions implying the existence of doubly chorded cycles without or with constraints

TL;DR

This paper establishes precise spectral criteria that guarantee the presence of doubly chorded cycles and related structures in graphs, addressing a question posed by Gould in 2022.

Contribution

It provides tight spectral conditions for the existence of doubly chorded cycles and variants, advancing understanding of spectral graph theory.

Findings

Spectral conditions for doubly chorded cycles

Spectral conditions for doubly chorded cycles with incident chords

Answer to Gould's 2022 question

Abstract

What spectral conditions imply a graph contains a chorded cycle? This question was asked by R.J. Gould in 2022. We answer two modified versions of Gould's question by giving tight spectral conditions that imply the existence of doubly chorded cycle, and a doubly chorded cycle with two chords incident to a vertex, respectively.