Extremal density for sparse minors and subdivisions

Abstract: We prove an asymptotically tight bound on the extremal density guaranteeing subdivisions of bounded-degree bipartite graphs with a separability condition. As corollaries, we answered several questions of Reed and Wood on embedding sparse minors. In particular, we prove that a graph with average degree $(3/2+ o(1))t$ contains every $t$-vertex planar graph as a minor and this constant $3/2$ is best possible. This is joint work with John Haslegrave and Hong Liu.

combinatorics

Audience: researchers in the topic

Comments: password 121323

SCMS Combinatorics Seminar

Series comments: Check scmscomb.github.io/ for more information