On Explicit Random-Like Tournaments

Random Knockout Tournaments

Full terms and conditions of use: http://pubsonline.informs.org/page/terms-and-conditions This article may be used only for the purposes of research, teaching, and/or private study. Commercial use or systematic downloading (by robots or other automatic processes) is prohibited without explicit Publisher approval, unless otherwise noted. For more information, contact [email protected]. The...

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 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.

On MAXCUT in strictly supercritical random graphs, and coloring of random graphs and random tournaments

We use a theorem by Ding, Lubetzky and Peres describing the structure of the giant component of random graphs in the strictly supercritical regime, in order to determine the typical size of MAXCUT of G ∼ G (