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

Date and Time: Thursday, April 15, 2010, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Ido Ben-Eliezer (Tel Aviv University)

On the size Ramsey number of directed path

We study the size Ramsey number of directed path of length n in oriented graphs, where no antiparallel edges are allowed. We give nearly tight bounds for every fixed number of colors, showing that for every q\geq 1 there are constant c,c_q such that \frac{c_q n^{2q}\log^{1/q} n}{\log^{(q+2)/q}\log n} \leq r_e(\overrightarrow{P_n},q+1) \leq c n^{2q}\log^{2}{n}. In particular this shows that the size Ramsey number in oriented graphs is asymptotically larger than the size Ramsey number in general directed graphs.

Joint work with Michael Krivelevich and Benny Sudakov.

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