{"id":{"repo_id":"aachen","oai_identifier":"oai:publications.rwth-aachen.de:49967"},"canonical_url":"https://search.dev.ndltd.org/etd/aachen/oai:publications.rwth-aachen.de:49967","repository":{"repo_id":"aachen","name":"RWTH Aachen University","base_url":"https://publications.rwth-aachen.de/oai2d"},"display":{"title":"Hamiltonian cycles in certain graphs and out-arc pancyclic vertices in tournaments","abstract":"In the first part of this thesis, some new sufficient conditions for a graph to be Hamiltonian and some other results on related topics are introduced. Generally speaking, there are two important types of sufficient conditions: the so-called degree conditions and the typical forbidden subgraph conditions. By combining those two types, some new sufficient conditions are found: 2-heavy and almost distance-hereditary graphs; claw-free graphs with an Ore-type condition; claw-free and hourglass-free graphs with a Fan-type condition. Moreover, this part deals with a conjecture introduced by Bang-Jensen and Gutin about the existence of a properly colored Hamiltonian path in an edge-colored complete graph, and deals with the existence of the complementary cycles in jump graphs. In the second part of this thesis, tournaments are considered . Yao, Guo and Zhang conjectured that each k-strong tournament contains k vertices whose out-arcs are pancyclic. They proved that this is true for k=1. In this thesis, the conjecture is also verified for k=2, 3. Yeo found an infinite class of k-strong tournaments, each of which contains at most 3 such vertices. This gives rise to an interesting problem: How many vertices does a tournament contain such that all out-arcs of those vertices are 4-pancyclic? At last, it is shown that each k-strong tournament with k>=2 contains at least k+1 vertices whose out-arcs are 4-pancyclic.","abstract_html":"In the first part of this thesis, some new sufficient conditions for a graph to be Hamiltonian and some other results on related topics are introduced. Generally speaking, there are two important types of sufficient conditions: the so-called degree conditions and the typical forbidden subgraph conditions. By combining those two types, some new sufficient conditions are found: 2-heavy and almost distance-hereditary graphs; claw-free graphs with an Ore-type condition; claw-free and hourglass-free graphs with a Fan-type condition. Moreover, this part deals with a conjecture introduced by Bang-Jensen and Gutin about the existence of a properly colored Hamiltonian path in an edge-colored complete graph, and deals with the existence of the complementary cycles in jump graphs. In the second part of this thesis, tournaments are considered . Yao, Guo and Zhang conjectured that each k-strong tournament contains k vertices whose out-arcs are pancyclic. They proved that this is true for k=1. In this thesis, the conjecture is also verified for k=2, 3. Yeo found an infinite class of k-strong tournaments, each of which contains at most 3 such vertices. This gives rise to an interesting problem: How many vertices does a tournament contain such that all out-arcs of those vertices are 4-pancyclic? At last, it is shown that each k-strong tournament with k&gt;=2 contains at least k+1 vertices whose out-arcs are 4-pancyclic.","abstract_has_math":false,"creators":["Feng, Jinfeng"],"institution":"Mainz","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Guo, Yubao"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008","date_published":"2008","updated_at":"2026-07-30T19:40:16Z","subjects":["info:eu-repo/classification/ddc/510","Turnier <Mathematik>","Hamilton-Kreis","Graphentheorie","Mathematik","graph theory","digraph","tournament","hamiltonian cycle"],"languages":["eng"],"rights":["info:eu-repo/semantics/openAccess"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112534%22"],"render_values":[{"text":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112534%22","href":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112534%22","code":true}]}]},"links":{"outbound_url":"https://publications.rwth-aachen.de/record/49967","outbound_label":"Repository record","outbound_source":"dc:identifier"},"source_record":{"url":"https://publications.rwth-aachen.de/oai2d?verb=GetRecord&metadataPrefix=oai_dc&identifier=oai%3Apublications.rwth-aachen.de%3A49967","prefix":"oai_dc"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Guo, Yubao"]},{"key":"dc:creator","label":"Author","values":["Feng, Jinfeng"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:coverage","label":"Dc Coverage","values":["DE"]},{"key":"dc:date","label":"Dc Date","values":["2008"]},{"key":"dc:publisher","label":"Institution","values":["Mainz"]},{"key":"dc:relation","label":"Dc Relation","values":["info:eu-repo/semantics/altIdentifier/isbn/3-86130-136-9","info:eu-repo/semantics/altIdentifier/issn/1437-6792","info:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-22110"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["info:eu-repo/classification/ddc/510","Turnier <Mathematik>","Hamilton-Kreis","Graphentheorie","Mathematik","graph theory","digraph","tournament","hamiltonian cycle"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://publications.rwth-aachen.de/record/49967","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112534%22"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In the first part of this thesis, some new sufficient conditions for a graph to be Hamiltonian and some other results on related topics are introduced. Generally speaking, there are two important types of sufficient conditions: the so-called degree conditions and the typical forbidden subgraph conditions. By combining those two types, some new sufficient conditions are found: 2-heavy and almost distance-hereditary graphs; claw-free graphs with an Ore-type condition; claw-free and hourglass-free graphs with a Fan-type condition. Moreover, this part deals with a conjecture introduced by Bang-Jensen and Gutin about the existence of a properly colored Hamiltonian path in an edge-colored complete graph, and deals with the existence of the complementary cycles in jump graphs. In the second part of this thesis, tournaments are considered . Yao, Guo and Zhang conjectured that each k-strong tournament contains k vertices whose out-arcs are pancyclic. They proved that this is true for k=1. In this thesis, the conjecture is also verified for k=2, 3. Yeo found an infinite class of k-strong tournaments, each of which contains at most 3 such vertices. This gives rise to an interesting problem: How many vertices does a tournament contain such that all out-arcs of those vertices are 4-pancyclic? At last, it is shown that each k-strong tournament with k>=2 contains at least k+1 vertices whose out-arcs are 4-pancyclic."]},{"key":"dc:source","label":"Dc Source","values":["Aachen : Mainz, Aachener Beiträge zur Mathematik 31, III, 114 S. : graph. Darst. (2008). = Zugl.: Aachen, Techn. Hochsch., Diss., 2008"]},{"key":"dc:title","label":"Title","values":["Hamiltonian cycles in certain graphs and out-arc pancyclic vertices in tournaments"]}]}],"canonical_facts":{"dc:contributor":["Guo, Yubao"],"dc:coverage":["DE"],"dc:creator":["Feng, Jinfeng"],"dc:date":["2008"],"dc:description":["In the first part of this thesis, some new sufficient conditions for a graph to be Hamiltonian and some other results on related topics are introduced. Generally speaking, there are two important types of sufficient conditions: the so-called degree conditions and the typical forbidden subgraph conditions. By combining those two types, some new sufficient conditions are found: 2-heavy and almost distance-hereditary graphs; claw-free graphs with an Ore-type condition; claw-free and hourglass-free graphs with a Fan-type condition. Moreover, this part deals with a conjecture introduced by Bang-Jensen and Gutin about the existence of a properly colored Hamiltonian path in an edge-colored complete graph, and deals with the existence of the complementary cycles in jump graphs. In the second part of this thesis, tournaments are considered . Yao, Guo and Zhang conjectured that each k-strong tournament contains k vertices whose out-arcs are pancyclic. They proved that this is true for k=1. In this thesis, the conjecture is also verified for k=2, 3. Yeo found an infinite class of k-strong tournaments, each of which contains at most 3 such vertices. This gives rise to an interesting problem: How many vertices does a tournament contain such that all out-arcs of those vertices are 4-pancyclic? At last, it is shown that each k-strong tournament with k>=2 contains at least k+1 vertices whose out-arcs are 4-pancyclic."],"dc:identifier":["https://publications.rwth-aachen.de/record/49967","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112534%22"],"dc:language":["eng"],"dc:publisher":["Mainz"],"dc:relation":["info:eu-repo/semantics/altIdentifier/isbn/3-86130-136-9","info:eu-repo/semantics/altIdentifier/issn/1437-6792","info:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-22110"],"dc:rights":["info:eu-repo/semantics/openAccess"],"dc:source":["Aachen : Mainz, Aachener Beiträge zur Mathematik 31, III, 114 S. : graph. Darst. (2008). = Zugl.: Aachen, Techn. Hochsch., Diss., 2008"],"dc:subject":["info:eu-repo/classification/ddc/510","Turnier <Mathematik>","Hamilton-Kreis","Graphentheorie","Mathematik","graph theory","digraph","tournament","hamiltonian cycle"],"dc:title":["Hamiltonian cycles in certain graphs and out-arc pancyclic vertices in tournaments"],"dc:type":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]},"updated_at":"2026-07-30T19:40:16Z"}