Chudnovsky–Scott–Seymour's Burling-control conjecture
A graph class is Burling-controlled when its chromatic complexity is controlled by the Burling graphs, as defined in the source. An induced subdivision of a graph is a subdivision appearing as an induced subgraph. Chudnovsky–Scott–Seymour's Burling-control conjecture. For every graph , the class of graphs excluding induced subdivisions of is Burling-controlled. This is proposed as a resuscitated form of Scott's refuted conjecture: Burling's construction is the only known obstruction to Scott's statement, and the conjecture remains open.
References
Primary source
Tara Abrishami, Marcin Briański, James Davies, Xiying Du, Jana Masaříková, Paweł Rzążewski and Bartosz Walczak, “Burling graphs in graphs with large chromatic number”, arXiv:2510.19650 (2025).
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