The induced-minor finite-asymptotic-dimension conjecture

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.

Sources & referencesView supporting material

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).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.