The induced-minor finite-asymptotic-dimension conjecture
For a graph , a graph class excludes as an induced minor when none of its graphs contains as an induced minor. A graph class has finite asymptotic dimension when its asymptotic dimension is finite. Induced-minor asymptotic-dimension conjecture. For every graph , the class of graphs excluding as an induced minor has finite asymptotic dimension. The conjecture generalizes a stated theorem on region intersection graphs; the special case where is a subdivision of is known, while the general case 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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