{"id":{"repo_id":"aachen","oai_identifier":"oai:publications.rwth-aachen.de:57026"},"canonical_url":"https://search.dev.ndltd.org/etd/aachen/oai:publications.rwth-aachen.de:57026","repository":{"repo_id":"aachen","name":"RWTH Aachen University","base_url":"https://publications.rwth-aachen.de/oai2d"},"display":{"title":"Regular factors in graphs","abstract":"The first part of this dissertation deals with the influence of different parameters on the existence of a regular factor in a regular graph. Sharp sufficient conditions for the existence of a regular factor are presented, if either the radius, the chromatic number or the vertex-connectivity of the graph are known, besides the order and the degree of the graph. The second part deals with the question how large the edge-set of a graph can be if the graph has a unique regular factor. The focus will be on extremal bipartite graphs with a unique regular factor. An analysis of the structure shows that all extremal bipartite graphs with a unique k-factor have exactly 2k vertices of minimum degree. This result allows for positive answers on the maximal number of edges in an extremal graph if k is small. This dissertation closes with results on extremal graphs with a unique [1,k]-factor.","abstract_html":"The first part of this dissertation deals with the influence of different parameters on the existence of a regular factor in a regular graph. Sharp sufficient conditions for the existence of a regular factor are presented, if either the radius, the chromatic number or the vertex-connectivity of the graph are known, besides the order and the degree of the graph. The second part deals with the question how large the edge-set of a graph can be if the graph has a unique regular factor. The focus will be on extremal bipartite graphs with a unique regular factor. An analysis of the structure shows that all extremal bipartite graphs with a unique k-factor have exactly 2k vertices of minimum degree. This result allows for positive answers on the maximal number of edges in an extremal graph if k is small. 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Sharp sufficient conditions for the existence of a regular factor are presented, if either the radius, the chromatic number or the vertex-connectivity of the graph are known, besides the order and the degree of the graph. The second part deals with the question how large the edge-set of a graph can be if the graph has a unique regular factor. The focus will be on extremal bipartite graphs with a unique regular factor. An analysis of the structure shows that all extremal bipartite graphs with a unique k-factor have exactly 2k vertices of minimum degree. This result allows for positive answers on the maximal number of edges in an extremal graph if k is small. This dissertation closes with results on extremal graphs with a unique [1,k]-factor."]},{"key":"dc:source","label":"Dc Source","values":["Aachen : Publikationsserver der RWTH Aachen University V, 70 S. (2002). = Aachen, Techn. Hochsch., Diss., 2002"]},{"key":"dc:title","label":"Title","values":["Regular factors in graphs"]}]}],"canonical_facts":{"dc:contributor":["Volkmann, Lutz"],"dc:coverage":["DE"],"dc:creator":["Hoffmann, Arne"],"dc:date":["2002"],"dc:description":["The first part of this dissertation deals with the influence of different parameters on the existence of a regular factor in a regular graph. Sharp sufficient conditions for the existence of a regular factor are presented, if either the radius, the chromatic number or the vertex-connectivity of the graph are known, besides the order and the degree of the graph. The second part deals with the question how large the edge-set of a graph can be if the graph has a unique regular factor. The focus will be on extremal bipartite graphs with a unique regular factor. An analysis of the structure shows that all extremal bipartite graphs with a unique k-factor have exactly 2k vertices of minimum degree. This result allows for positive answers on the maximal number of edges in an extremal graph if k is small. This dissertation closes with results on extremal graphs with a unique [1,k]-factor."],"dc:identifier":["https://publications.rwth-aachen.de/record/57026","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-119096%22"],"dc:language":["eng"],"dc:publisher":["Publikationsserver der RWTH Aachen University"],"dc:relation":["info:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-3897"],"dc:rights":["info:eu-repo/semantics/openAccess"],"dc:source":["Aachen : Publikationsserver der RWTH Aachen University V, 70 S. (2002). = Aachen, Techn. Hochsch., Diss., 2002"],"dc:subject":["info:eu-repo/classification/ddc/510","Mathematik"],"dc:title":["Regular factors in graphs"],"dc:type":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]},"updated_at":"2026-07-30T19:42:01Z"}