{"id":{"repo_id":"whiterose","oai_identifier":"oai:etheses.whiterose.ac.uk:1750"},"canonical_url":"https://search.dev.ndltd.org/etd/whiterose/oai:etheses.whiterose.ac.uk:1750","repository":{"repo_id":"whiterose","name":"White Rose University Consortium","base_url":"https://etheses.whiterose.ac.uk/cgi/oai2"},"display":{"title":"Classification of Countable Homogeneous 2-Graphs","abstract":"We classify certain families of homogeneous 2-graphs and prove some results that apply to families of 2-graphs that we have not completely classified. We classify homogeneous 2-coloured 2-graphs where one component is a disjoint union of complete graphs and the other is the random graph or the generic Kr-free graph for some r. We show that any non-trivial examples are derived from a homogeneous 2-coloured 2-graph where one component is the complete graph and the other is the random graph or the generic Kr-free graph for some r; and these are in turn either generic or equivalent to one that minimally omits precisely one monochromatic colour-1 (K1,Kt) 2-graph for some t < r. We also classify homogeneous 2-coloured 2-graphs G where both components are isomorphic and each is either the random graph or the generic K3-free graph; in both cases show that there is an antichain A of monochromatic colour-1 2-graphs all of the form (Ks,Kt) (for some s and t) such that G is equivalent to the homogeneous 2-coloured 2-graph with the specified components that is generic subject to minimally omitting the elements of A.","abstract_html":"We classify certain families of homogeneous 2-graphs and prove some results that apply to families of 2-graphs that we have not completely classified. We classify homogeneous 2-coloured 2-graphs where one component is a disjoint union of complete graphs and the other is the random graph or the generic Kr-free graph for some r. We show that any non-trivial examples are derived from a homogeneous 2-coloured 2-graph where one component is the complete graph and the other is the random graph or the generic Kr-free graph for some r; and these are in turn either generic or equivalent to one that minimally omits precisely one monochromatic colour-1 (K1,Kt) 2-graph for some t &lt; r. We also classify homogeneous 2-coloured 2-graphs G where both components are isomorphic and each is either the random graph or the generic K3-free graph; in both cases show that there is an antichain A of monochromatic colour-1 2-graphs all of the form (Ks,Kt) (for some s and t) such that G is equivalent to the homogeneous 2-coloured 2-graph with the specified components that is generic subject to minimally omitting the elements of A.","abstract_has_math":false,"creators":["Rose, Simon Edward"],"institution":"University of Leeds","degree_name":"Ph.D","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Truss, J."],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-03","date_published":"2011-03","updated_at":"2026-07-24T06:05:10Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["uk.bl.ethos.539681"],"render_values":[{"text":"uk.bl.ethos.539681","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Truss, J."]},{"key":"dc:creator","label":"Author","values":["Rose, Simon Edward"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-03"]},{"key":"dc:date.issued","label":"Date","values":["2011-03"]},{"key":"dc:publisher.commercial","label":"Dc Publisher Commercial","values":["University of Leeds"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Pure Mathematics (Leeds)"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Leeds"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://etheses.whiterose.ac.uk/id/eprint/1750/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Ph.D"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["uk.bl.ethos.539681"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://etheses.whiterose.ac.uk/id/eprint/1750/1/Rose_SE_Mathematics_PhD_2011.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We classify certain families of homogeneous 2-graphs and prove some results that apply to families of 2-graphs that we have not completely classified. We classify homogeneous 2-coloured 2-graphs where one component is a disjoint union of complete graphs and the other is the random graph or the generic Kr-free graph for some r. We show that any non-trivial examples are derived from a homogeneous 2-coloured 2-graph where one component is the complete graph and the other is the random graph or the generic Kr-free graph for some r; and these are in turn either generic or equivalent to one that minimally omits precisely one monochromatic colour-1 (K1,Kt) 2-graph for some t < r. We also classify homogeneous 2-coloured 2-graphs G where both components are isomorphic and each is either the random graph or the generic K3-free graph; in both cases show that there is an antichain A of monochromatic colour-1 2-graphs all of the form (Ks,Kt) (for some s and t) such that G is equivalent to the homogeneous 2-coloured 2-graph with the specified components that is generic subject to minimally omitting the elements of A."]},{"key":"dc:format","label":"Dc Format","values":["text"]},{"key":"dc:title","label":"Title","values":["Classification of Countable Homogeneous 2-Graphs"]}]}],"canonical_facts":{"dc:contributor.advisor":["Truss, J."],"dc:creator":["Rose, Simon Edward"],"dc:date":["2011-03"],"dc:date.issued":["2011-03"],"dc:description.abstract":["We classify certain families of homogeneous 2-graphs and prove some results that apply to families of 2-graphs that we have not completely classified. We classify homogeneous 2-coloured 2-graphs where one component is a disjoint union of complete graphs and the other is the random graph or the generic Kr-free graph for some r. We show that any non-trivial examples are derived from a homogeneous 2-coloured 2-graph where one component is the complete graph and the other is the random graph or the generic Kr-free graph for some r; and these are in turn either generic or equivalent to one that minimally omits precisely one monochromatic colour-1 (K1,Kt) 2-graph for some t < r. We also classify homogeneous 2-coloured 2-graphs G where both components are isomorphic and each is either the random graph or the generic K3-free graph; in both cases show that there is an antichain A of monochromatic colour-1 2-graphs all of the form (Ks,Kt) (for some s and t) such that G is equivalent to the homogeneous 2-coloured 2-graph with the specified components that is generic subject to minimally omitting the elements of A."],"dc:format":["text"],"dc:identifier":["uk.bl.ethos.539681"],"dc:identifier.uri":["https://etheses.whiterose.ac.uk/id/eprint/1750/1/Rose_SE_Mathematics_PhD_2011.pdf"],"dc:publisher.commercial":["University of Leeds"],"dc:publisher.department":["Pure Mathematics (Leeds)"],"dc:publisher.institution":["University of Leeds"],"dc:relation.isreferencedby":["https://etheses.whiterose.ac.uk/id/eprint/1750/"],"dc:title":["Classification of Countable Homogeneous 2-Graphs"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["Ph.D"]},"updated_at":"2026-07-24T06:05:10Z"}