On Hamilton Decompositions

TL;DR

This paper investigates Hamilton decompositions of diregular tournaments, proving the conjecture for prime-sized cases and proposing a general method for certain tournaments.

Contribution

It confirms Kelly's conjecture for prime-sized diregular tournaments and introduces a general approach for Hamilton decompositions in specific cases.

Findings

Decomposition possible when (2n+1) is prime

Method does not work for non-prime (2n+1)

Proposes a general method for certain tournament sizes

Abstract

P. J. Kelly conjectured in 1968 that every diregular tournament on (2n+1) points can be decomposed in directed Hamilton circuits [1]. We define so called leading diregular tournament on (2n+1) points and show that it can be decomposed in directed Hamilton circuits when (2n+1) is a prime number. When (2n+1) is not a prime number this method does not work and we will need to devise some another method. We also propose a general method to find Hamilton decomposition of certain tournament for all sizes.