Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.760517
Title: Large structures in dense directed graphs
Author: Naia dos Santos, Tassio
ISNI:       0000 0004 7432 5078
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2018
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Abstract:
We answer questions in extremal combinatorics, for directed graphs. Specifically, we investigate which large tree-like directed graphs are contained in all dense directed graphs of large order. More precisely, let T be an oriented tree of order n; among others, we establish the following results. (1) We obtain a sufficient condition which ensures every tournament of order n contains T, and show that almost every tree possesses this property. (2) We prove that for all positive C, ɛ and sufficiently large n, every tournament of order (1+ɛ)n contains T if Δ(T)≤(log n)^C. (3) We prove that for all positive Δ, ɛ and sufficiently large n, every directed graph G of order n and minimum semidegree (1/2+ɛ)n contains T if Δ(T)≤Δ. (4) We obtain a sufficient condition which ensures that every directed graph G of order n with minimum semidegree at least (1/2+ɛ)n contains T, and show that almost every tree possesses this property. (5) We extend our method in (4) to a class of tree-like spanning graphs which includes all orientations of Hamilton cycles and large subdivisions of any graph. Result (1) confirms a conjecture of Bender and Wormald and settles a conjecture of Havet and Thomassé for almost every tree; (2) strengthens a result of Kühn, Mycroft and Osthus; (3) is a directed graph analogue of a classical result of Komlós, Sárközy and Szemerédi and is implied by (4) and (5) is of independent interest.
Supervisor: Not available Sponsor: Ciencia sem Fronteiras CNPq
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.760517  DOI: Not available
Keywords: QA Mathematics
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