Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.520351
Title: On cycles in directed graphs
Author: Kelly, Luke Tristian
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2010
Availability of Full Text:
Access from EThOS:
Access from Institution:
Abstract:
The main results of this thesis are the following. We show that for each alpha > 0 every sufficiently large oriented graph G with minimum indegree and minimum outdegree at least 3 |G| / 8 + alpha |G| contains a Hamilton cycle. This gives an approximate solution to a problem of Thomassen. Furthermore, answering completely a conjecture of Haggkvist and Thomason, we show that we get every possible orientation of a Hamilton cycle. We also deal extensively with short cycles, showing that for each l > 4 every sufficiently large oriented graph G with minimum indegree and minimum outdegree at least |G| / 3 + 1 contains an l-cycle. This is best possible for all those l > 3 which are not divisible by 3. Surprisingly, for some other values of l, an l-cycle is forced by a much weaker minimum degree condition. We propose and discuss a conjecture regarding the precise minimum degree which forces an l-cycle (with l > 3 divisible by 3) in an oriented graph. We also give an application of our results to pancyclicity.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.520351  DOI: Not available
Keywords: QA Mathematics
Share: