When all holes have the same length

TL;DR

This paper characterizes the structure of graphs where all chordless cycles of length at least 4 are of a fixed length , providing insights into their composition for all  .

Contribution

It offers a comprehensive structural description of graphs with uniform chordless cycle lengths for all  , extending understanding of such graph classes.

Findings

Structural description for graphs with all chordless cycles of length .

Applicable for all  , \u0017 .

Enhances classification of graphs based on cycle lengths.

Abstract

For every integer $\ell \geq 7$, we give a structural description of the class of graphs whose chordless cycles of length at least 4 all have length $\ell$.