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

Date and Time: Tuesday, March 26, 2019, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Charlotte Knierim

Improved bounds on the multicolor Ramsey number of paths and even cycles

We study the multicolor Ramsey numbers for paths and even cycles, Rk(Pn) and Rk(Cn), which are the smallest integers N such that every coloring of the complete graph KN has a monochromatic copy of Pn or Cn respectively. For a long time, Rk(Pn) has only been known to lie between (k−1+o(1))n and (k+o(1))n. A recent breakthrough by Sárközy and later improvement by Davies, Jenssen and Roberts give an upper bound of (k−1/4+o(1))n. We improve the upper bound to (k−1/2+o(1))n. Our approach uses structural insights in connected graphs without a large matching. This is joint work with Pascal Su.

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