Graphs with all holes the same length

Linda Cook, Jake Horsfield, Myriam Preissmann, Cléophée Robin, Paul Seymour, Ni Luh Dewi Sintiari, Nicolas Trotignon, Kristina Vušković

Published 2021-10-19, updated 2023-05-24Version 2

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 $\ell\ge 7$.