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On the Structure of Counterexamples to the Coloring Conjecture of Hajós

Hajós conjectured that, for any positive integer
k, every graph containing no K_(k+1)-subdivision is k-colorable. This is true when k is at most three, and false when k exceeds six. Hajós' conjecture remains open for k=4,5.


We will first present some known results on Hajós' conjecture. Then we derive a result on the structure of 2-connected graphs

with no cycle through three specified vertices. This result will then be used for the proof of the main result of this thesis. We show that any possible counterexample to Hajós' conjecture for

k=4 with minimum number of vertices must be 4-connected. This is

a step in an attempt to reduce Hajós' conjecture for k=4 to the conjecture of Seymour that any 5-connected non-planar graph contains a K_5-subdivision.

Identiferoai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/4994
Date20 May 2004
CreatorsZickfeld, Florian
PublisherGeorgia Institute of Technology
Source SetsGeorgia Tech Electronic Thesis and Dissertation Archive
Languageen_US
Detected LanguageEnglish
TypeThesis
Format276328 bytes, application/pdf

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