{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86869"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86869","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Topics in Stochastic Combinatorial Optimization and Extremal Graph Theory","abstract":"We consider a random geometric graph, G(n, r ), constructed by placing points randomly in a square S n of area n according to a Poisson process of intensity 1, and adding an edge joining any pair of points at most distance r=r(n) apart according to the ℓinfinity -metric. We show that w.h.p. this random geometric graph contains a Hamiltonian cycle if it is 2-connected.","abstract_html":"We consider a random geometric graph, G(n, r ), constructed by placing points randomly in a square S n of area n according to a Poisson process of intensity 1, and adding an edge joining any pair of points at most distance r=r(n) apart according to the ℓinfinity -metric. We show that w.h.p. this random geometric graph contains a Hamiltonian cycle if it is 2-connected.","abstract_has_math":false,"creators":["Kaul, Hemanshu"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Jacobson, Sheldon H.","West, Douglas B."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:19:56Z","date_published":"2015-09-28T15:19:56Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3242891"],"render_values":[{"text":"(MiAaPQ)AAI3242891","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86869","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jacobson, Sheldon H.","West, Douglas B."]},{"key":"dc:creator","label":"Author","values":["Kaul, Hemanshu"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:19:56Z","10000-01-01","2006"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86869","(MiAaPQ)AAI3242891"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We consider a random geometric graph, G(n, r ), constructed by placing points randomly in a square S n of area n according to a Poisson process of intensity 1, and adding an edge joining any pair of points at most distance r=r(n) apart according to the ℓinfinity -metric. We show that w.h.p. this random geometric graph contains a Hamiltonian cycle if it is 2-connected.","Made available in DSpace on 2015-09-28T15:19:56Z (GMT). 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We show that w.h.p. this random geometric graph contains a Hamiltonian cycle if it is 2-connected.","Made available in DSpace on 2015-09-28T15:19:56Z (GMT). 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