Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, March 23, 2017, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Richard Montgomery (Trinity College, Cambridge)

Subdivisions in $C_4$-free graphs

Bollobás and Thomason, and independently Komlós and Szemerédi, showed in 1994 that any graph $G$ with average degree $d(G)$ contains a subdivision of a clique with at least $c\sqrt{d(G)}$ vertices, for some universal constant $c>0$. In 1999, Mader conjectured that $C_4$-free graphs $G$ in fact contain a subdivision of a larger clique, one with at least $c d(G)$ vertices, for some universal constant $c>0$. I will discuss a proof of this conjecture as well as a generalisation concerning $K_{s,t}$-free graphs. This is joint work with Hong Liu.

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