Resource type
Thesis type
(Thesis) M.Sc.
Date created
2017-08-08
Authors/Contributors
Author (aut): Halasz, Kevin Callanan
Abstract
The chromatic number of a latin square L, denoted χ(L), is defined as the minimum number of partial transversals needed to cover all of its cells. It has been conjectured that every latin square L satisfies χ(L) ≤ |L| + 2. If true, this would resolve a longstanding conjecture, commonly attributed to Brualdi, that every latin square has a partial transversal of length |L|−1. Restricting our attention to Cayley tables of finite groups, we prove two results. First, we constructively show that all finite Abelian groups G have Cayley tables with chromatic number |G|+2. Second, we give an upper bound for the chromatic number of Cayley tables of arbitrary finite groups. For |G| ≥ 3, this improves the best-known general upper bound from 2|G| to 3 |G|, while yielding an even stronger result in infinitely many cases.
Document
Identifier
etd10353
Copyright statement
Copyright is held by the author.
Scholarly level
Supervisor or Senior Supervisor
Thesis advisor (ths): Goddyn, Luis
Member of collection
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