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math.CO2020
Strong complete minors in digraphs
Maria Axenovich, António Girão, Richard Snyder +1
Kostochka and Thomason independently showed that any graph with average degree contains a minor. In particular, any graph with chromatic number $Ω(r\sqrt{…
math.CO2020
The Erdős-Hajnal conjecture for three colors and multiple forbidden patterns
Maria Axenovich, Richard Snyder, Lea Weber
Erdős and Szekeres's quantitative version of Ramsey's theorem asserts that any complete graph on n vertices that is edge-colored with two colors has a monochromatic clique on at le…
math.CO2020
Bipartite independence number in graphs with bounded maximum degree
Maria Axenovich, Jean-Sébastien Sereni, Richard Snyder +1
We consider a natural, yet seemingly not much studied, extremal problem in bipartite graphs. A bi-hole of size in a bipartite graph is a copy of in the bipartite…