Polynomial-time recognition and maximum independent set in Burling graphs
Combinatorics
2026-04-28 v2 Discrete Mathematics
Abstract
A Burling graph is an induced subgraph of some graph in Burling's construction of triangle-free high-chromatic graphs. Equivalently, a Burling graph is a graph that admits a so-called strict frame representation. We provide a polynomial-time algorithm to decide whether a given graph is a Burling graph and if it is, to construct its strict frame representation. The representation then enables a polynomial-time algorithm for the maximum independent set problem in Burling graphs. As a consequence, we establish Burling graphs as the first known hereditary class of graphs that admits such an algorithm while not being -bounded.
Keywords
Cite
@article{arxiv.2407.16666,
title = {Polynomial-time recognition and maximum independent set in Burling graphs},
author = {Paweł Rzążewski and Bartosz Walczak},
journal= {arXiv preprint arXiv:2407.16666},
year = {2026}
}