{"id":{"repo_id":"birmingham","oai_identifier":"oai:etheses.bham.ac.uk:1345"},"canonical_url":"https://search.dev.ndltd.org/etd/birmingham/oai:etheses.bham.ac.uk:1345","repository":{"repo_id":"birmingham","name":"University of Birmingham","base_url":"https://etheses.bham.ac.uk/cgi/oai2"},"display":{"title":"Embedding problems in graphs and hypergraphs","abstract":"The first part of this thesis concerns perfect matchings and their generalisations. We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph, thereby answering a question of Hàn, Person and Schacht. We say that a graph \\(G\\) has a perfect \\(H\\)-packing (also called an \\(H\\) - factor) if there exists a set of disjoint copies of \\(H\\) in \\(G\\) which together cover all the vertices of \\(G\\). Given a graph \\(H\\), we determine, asymptotically, the Ore-type degree condition which ensures that a graph \\(G\\) has a perfect \\(H\\)-packing. The second part of the thesis concerns Hamilton cycles in directed graphs. We give a condition on the degree sequences of a digraph \\(G\\) that ensures \\(G\\) is Hamiltonian. This gives an approximate solution to a problem of Nash-Williams concerning a digraph analogue of Chvatal's theorem. We also show that every sufficiently large regular tournament can almost completely be decomposed into edge-disjoint Hamilton cycles. More precisely, for each \\(\\eta\\) >0 every regular tournament \\(G\\) of sufficiently large order n contains at least (1/2- \\(\\eta\\))n edge-disjoint Hamilton cycles. This gives an approximate solution to a conjecture of Kelly from 1968.","abstract_html":"The first part of this thesis concerns perfect matchings and their generalisations. We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph, thereby answering a question of Hàn, Person and Schacht. We say that a graph \\(G\\) has a perfect \\(H\\)-packing (also called an \\(H\\) - factor) if there exists a set of disjoint copies of \\(H\\) in \\(G\\) which together cover all the vertices of \\(G\\). Given a graph \\(H\\), we determine, asymptotically, the Ore-type degree condition which ensures that a graph \\(G\\) has a perfect \\(H\\)-packing. The second part of the thesis concerns Hamilton cycles in directed graphs. We give a condition on the degree sequences of a digraph \\(G\\) that ensures \\(G\\) is Hamiltonian. This gives an approximate solution to a problem of Nash-Williams concerning a digraph analogue of Chvatal's theorem. We also show that every sufficiently large regular tournament can almost completely be decomposed into edge-disjoint Hamilton cycles. More precisely, for each \\(\\eta\\) >0 every regular tournament \\(G\\) of sufficiently large order n contains at least (1/2- \\(\\eta\\))n edge-disjoint Hamilton cycles. This gives an approximate solution to a conjecture of Kelly from 1968.","abstract_has_math":true,"creators":["Treglown, Andrew Clark"],"institution":"University of Birmingham","degree_name":"d_ph","degree_level":"d_ph","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-07","date_published":"2011-07","updated_at":"2026-07-24T01:11:29Z","subjects":["QA Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.sponsor","label":"Sponsor","values":["na"]},{"key":"dc:creator","label":"Author","values":["Treglown, Andrew Clark"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-07"]},{"key":"dc:date.issued","label":"Date","values":["2011-07"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["College of Engineering & Physical Sciences","School of Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Birmingham"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["http://etheses.bham.ac.uk//id/eprint/1345/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["d_ph"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["d_ph"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["QA Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://etheses.bham.ac.uk//id/eprint/1345/1/Treglown11PhD.pdf","http://etheses.bham.ac.uk//id/eprint/1345/2/Decl_IS_Treglown11PhD.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The first part of this thesis concerns perfect matchings and their generalisations. We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph, thereby answering a question of Hàn, Person and Schacht. We say that a graph \\(G\\) has a perfect \\(H\\)-packing (also called an \\(H\\) - factor) if there exists a set of disjoint copies of \\(H\\) in \\(G\\) which together cover all the vertices of \\(G\\). Given a graph \\(H\\), we determine, asymptotically, the Ore-type degree condition which ensures that a graph \\(G\\) has a perfect \\(H\\)-packing. The second part of the thesis concerns Hamilton cycles in directed graphs. We give a condition on the degree sequences of a digraph \\(G\\) that ensures \\(G\\) is Hamiltonian. This gives an approximate solution to a problem of Nash-Williams concerning a digraph analogue of Chvatal's theorem. We also show that every sufficiently large regular tournament can almost completely be decomposed into edge-disjoint Hamilton cycles. More precisely, for each \\(\\eta\\) >0 every regular tournament \\(G\\) of sufficiently large order n contains at least (1/2- \\(\\eta\\))n edge-disjoint Hamilton cycles. This gives an approximate solution to a conjecture of Kelly from 1968."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Embedding problems in graphs and hypergraphs"]}]}],"canonical_facts":{"dc:contributor.sponsor":["na"],"dc:creator":["Treglown, Andrew Clark"],"dc:date":["2011-07"],"dc:date.issued":["2011-07"],"dc:description.abstract":["The first part of this thesis concerns perfect matchings and their generalisations. We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph, thereby answering a question of Hàn, Person and Schacht. We say that a graph \\(G\\) has a perfect \\(H\\)-packing (also called an \\(H\\) - factor) if there exists a set of disjoint copies of \\(H\\) in \\(G\\) which together cover all the vertices of \\(G\\). Given a graph \\(H\\), we determine, asymptotically, the Ore-type degree condition which ensures that a graph \\(G\\) has a perfect \\(H\\)-packing. The second part of the thesis concerns Hamilton cycles in directed graphs. We give a condition on the degree sequences of a digraph \\(G\\) that ensures \\(G\\) is Hamiltonian. This gives an approximate solution to a problem of Nash-Williams concerning a digraph analogue of Chvatal's theorem. We also show that every sufficiently large regular tournament can almost completely be decomposed into edge-disjoint Hamilton cycles. More precisely, for each \\(\\eta\\) >0 every regular tournament \\(G\\) of sufficiently large order n contains at least (1/2- \\(\\eta\\))n edge-disjoint Hamilton cycles. This gives an approximate solution to a conjecture of Kelly from 1968."],"dc:format":["application/pdf"],"dc:identifier.uri":["http://etheses.bham.ac.uk//id/eprint/1345/1/Treglown11PhD.pdf","http://etheses.bham.ac.uk//id/eprint/1345/2/Decl_IS_Treglown11PhD.pdf"],"dc:publisher.department":["College of Engineering & Physical Sciences","School of Mathematics"],"dc:publisher.institution":["University of Birmingham"],"dc:relation.isreferencedby":["http://etheses.bham.ac.uk//id/eprint/1345/"],"dc:subject":["QA Mathematics"],"dc:title":["Embedding problems in graphs and hypergraphs"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["d_ph"],"dc:type.qualificationname":["d_ph"]},"updated_at":"2026-07-24T01:11:29Z"}