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

Date and Time: Thursday, May 31, 2007, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Jiří Matoušek (Charles Univ., Prague)

Large Monochromatic Components in Two-colored Grids

We consider the d-dimensional grid with diagonals, that is, the graph whose vertex set is [n]^d and two vertices are connected by an edge exactly if they differ by at most 1 in every coordinate. We prove that under every 2-coloring of the vertex set, there is a monochromatic connected subgraph with at least n^{d-1}-d^2 n^{d-2} vertices. This almost matches the obvious upper bound of n^{d-1}, obtained from the "horizontal layer" coloring. We also study a similar question for triangulated d-dimensional grids.

Joint work with Aleš Přívětivý.

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