Imperfections in Random Tournaments

Imperfections in Random Tournaments

Monochromatic paths in random tournaments

We prove that, with high probability, any 2-edge-colouring of a random tournament on n vertices contains a monochromatic path of length Ω(n/ √ log n). This resolves a conjecture of Ben-Eliezer, Krivelevich and Sudakov and implies a nearly tight upper bound on the oriented size Ramsey number of a directed path.

Random Knockout Tournaments

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Random Sampling of Labeled Tournaments

This note extends a recent result of Kannan, Tetali and Vempala to completely solve, via a simple proof, the problem of random generation of a labeled tournament with a given score vector. The proof uses the method of path coupling applied to an appropriate Markov chain on the set of labeled tournaments with the same score vector. MRS: 65C05, 05C20.

Intersections of random hypergraphs and tournaments

Given two random hypergraphs, or two random tournaments of order n, how much (or little) can we make them overlap by placing them on the same vertex set? We give asymptotic answers to this question.