{"id":{"repo_id":"etsu","oai_identifier":"oai:dc.etsu.edu:etd-2347"},"canonical_url":"https://search.dev.ndltd.org/etd/etsu/oai:dc.etsu.edu:etd-2347","repository":{"repo_id":"etsu","name":"East Tennessee State University","base_url":"https://dc.etsu.edu/do/oai/"},"display":{"title":"Packings and Coverings of Complete Graphs with a Hole with the 4-Cycle with a Pendant Edge","abstract":"<p>In this thesis, we consider packings and coverings of various complete graphs with the 4-cycle with a pendant edge. We consider both restricted and unrestricted coverings. Necessary and sufficient conditions are given for such structures for (1) complete graphs K<sub>v, </sub>(2) complete bipartite graphs K<sub>m,n</sub>, and (3) complete graphs with a hole K(v,w).</p>","abstract_html":"&lt;p&gt;In this thesis, we consider packings and coverings of various complete graphs with the 4-cycle with a pendant edge. We consider both restricted and unrestricted coverings. Necessary and sufficient conditions are given for such structures for (1) complete graphs K&lt;sub&gt;v, &lt;/sub&gt;(2) complete bipartite graphs K&lt;sub&gt;m,n&lt;/sub&gt;, and (3) complete graphs with a hole K(v,w).&lt;/p&gt;","abstract_has_math":false,"creators":["Xia, Yan"],"institution":null,"degree_name":"MS (Master of Science)","degree_level":"Thesis - unrestricted","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-08-01T07:00:00Z","date_published":"2013-08-01T07:00:00Z","updated_at":"2026-07-24T02:19:59Z","subjects":["graph theory","packing","covering","bipartite graph","decomposition","4-cycle","Discrete Mathematics and Combinatorics","Other Applied Mathematics"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/1173","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Xia, Yan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-04-29T07:00:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2013-08-01T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - unrestricted"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS (Master of Science)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["graph theory","packing","covering","bipartite graph","decomposition","4-cycle","Discrete Mathematics and Combinatorics","Other Applied Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright by the authors."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dc.etsu.edu/context/etd/article/2347/viewcontent/XiaY052113f.pdf","https://dc.etsu.edu/etd/1173"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>In this thesis, we consider packings and coverings of various complete graphs with the 4-cycle with a pendant edge. We consider both restricted and unrestricted coverings. Necessary and sufficient conditions are given for such structures for (1) complete graphs K<sub>v, </sub>(2) complete bipartite graphs K<sub>m,n</sub>, and (3) complete graphs with a hole K(v,w).</p>"]},{"key":"dc:title","label":"Title","values":["Packings and Coverings of Complete Graphs with a Hole with the 4-Cycle with a Pendant Edge"]}]}],"canonical_facts":{"dc:creator":["Xia, Yan"],"dc:date.available":["2013-04-29T07:00:00Z"],"dc:date.issued":["2013-08-01T07:00:00Z"],"dc:description.abstract":["<p>In this thesis, we consider packings and coverings of various complete graphs with the 4-cycle with a pendant edge. We consider both restricted and unrestricted coverings. Necessary and sufficient conditions are given for such structures for (1) complete graphs K<sub>v, </sub>(2) complete bipartite graphs K<sub>m,n</sub>, and (3) complete graphs with a hole K(v,w).</p>"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/2347/viewcontent/XiaY052113f.pdf","https://dc.etsu.edu/etd/1173"],"dc:rights":["Copyright by the authors."],"dc:subject":["graph theory","packing","covering","bipartite graph","decomposition","4-cycle","Discrete Mathematics and Combinatorics","Other Applied Mathematics"],"dc:title":["Packings and Coverings of Complete Graphs with a Hole with the 4-Cycle with a Pendant Edge"],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:19:59Z"}