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math.CO2026
Asymptotic dimension of graphs excluding an induced or fat minor
Robert Hickingbotham, Freddie Illingworth, Piotr Micek +1
Asymptotic dimension is a large-scale invariant of metric spaces that was introduced by Gromov (1993). A major open problem in coarse graph theory asks whether, for every fixed gra…
math.CO2026
On the solution to the Erdős-Hajnal problem on high-girth high-chromatic subgraphs
Tung Nguyen, Bartosz Walczak
A well-known problem of Erdős and Hajnal from the 1960s asks whether every graph with huge chromatic number contains a subgraph with large girth and large chromatic number. Very re…