Graphs with all holes the same length

TL;DR

This paper characterizes the structure of graphs where all induced cycles of length four or more are exactly of length 6, providing a complete description for each 67.

Contribution

It offers a comprehensive classification of 6-holed graphs for all 67, advancing understanding of their structural properties.

Findings

Complete description of 6-holed graphs for each 67

Structural characterization of graphs with uniform cycle lengths

Advances in graph theory related to induced cycles

Abstract

A graph is "$\ell$-holed" if all its induced cycles of length at least four have length exactly $\ell$. We give a complete description of the $\ell$-holed graphs for each $\ell\ge 7$.