Coloring cayley tables of finite groups

Date created: 
2017-08-08
Identifier: 
etd10353
Keywords: 
Latin square (05B15)
Graph coloring (05C15)
Strongly regular graphs (05E30)
Cayley table
Partial transversal
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 type: 
Thesis
Rights: 
This thesis may be printed or downloaded for non-commercial research and scholarly purposes. Copyright remains with the author.
File(s): 
Senior supervisor: 
Luis Goddyn
Department: 
Science: Department of Mathematics
Thesis type: 
(Thesis) M.Sc.
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