The induced-minor finite-asymptotic-dimension conjecture
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.
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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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