Speaker
Linda Cook
(IBS DIMAG)
Description
We call an induced cycle of length at least four a hole. The parity of a hole is the parity of its length. Forbidding holes of certain types in a graph has deep structural implications. In 2006, Chudnovksy, Seymour, Robertson, and Thomas famously proved that a graph is perfect if and only if it does not contain an odd hole or a complement of an odd hole. In 2002, Conforti, Cornuéjols, Kapoor, and Vušković provided a structural description of the class of even-hole-free graphs. I will describe the structure of all graphs that contain only holes of length $\ell$ for every $\ell \geq 7$ (joint work with Jake Horsfield, Myriam Preissmann, Paul Seymour, Ni Luh Dewi Sintiari, Cléophée Robin, Nicolas Trotignon, and Kristina Vušković.
Primary author
Linda Cook
(IBS DIMAG)
