A Direct Construction of Nontransitive Dice Sets. Issue 11 (19th June 2017) - Angel, Levi; Davis, Matt
Abstract: In this paper, we give a direct construction for a set of dice realizing any given tournament T . The construction for a tournament with n vertices requires dice with n sides if n is odd, n + 1 sides if n is divisible by 4, and n − 1 sides if n ≡ 2 mod 4. This appears to be the most efficient general construction to date. Our construction relies only on a standard construction from graph theory.