Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, October 23, 2018, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Matija Bucic

Nearly-linear monotone paths in edge-ordered graphs

How long a monotone path can one always find in any edge-ordering of the complete graph K_n? This appealing question was first asked by Chvátal and Komlós in 1971, and has since attracted the attention of many researchers, inspiring a variety of related problems. The prevailing conjecture is that one can always find a monotone path of linear length, but until now the best known lower bound was n^2/3-o(1). We almost close this gap, proving that any edge-ordering of the complete graph contains a monotone path of length n^1-o(1). This is joint work with Matthew Kwan, Alexey Pokrovskiy, Benny Sudakov, Tuan Tran and Adam Zsolt Wagner.

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