Detecting a long even hole

TL;DR

This paper presents a polynomial-time algorithm to detect the presence of long even induced cycles in graphs, advancing graph theory and algorithmic graph analysis.

Contribution

It introduces a new polynomial-time method for detecting long even holes in graphs, which was previously unresolved.

Findings

Efficient detection of long even cycles in polynomial time

Algorithm works for cycles of length at least 4

Advances understanding of graph cycle structures

Abstract

For each integer $\ell \geq 4$, we give a polynomial-time algorithm to test whether a graph contains an induced cycle with length at least $\ell$ and even