The induced-minor finite-asymptotic-dimension conjecture

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For a graph FF, a graph class excludes FF as an induced minor when none of its graphs contains FF 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 FF, the class of graphs excluding FF as an induced minor has finite asymptotic dimension. The conjecture generalizes a stated theorem on region intersection graphs; the special case where FF is a subdivision of K4K_4 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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