{"id":{"repo_id":"etsu","oai_identifier":"oai:dc.etsu.edu:etd-3392"},"canonical_url":"https://search.dev.ndltd.org/etd/etsu/oai:dc.etsu.edu:etd-3392","repository":{"repo_id":"etsu","name":"East Tennessee State University","base_url":"https://dc.etsu.edu/do/oai/"},"display":{"title":"Packings and Coverings of Various Complete Digraphs with the Orientations of a 4-Cycle.","abstract":"<p>There are four orientations of cycles on four vertices. Necessary and sufficient conditions are given for covering complete directed digraphs <em>D<sub>v</sub></em>, packing and covering complete bipartite digraphs, <em>D<sub>m,n</sub></em>, and packing and covering the complete digraph on <em>v</em> vertices with hole of size <em>w</em>, <em>D</em>(<em>v</em>,<em>w</em>), with three of the orientations of a 4-cycle, including <em>C</em><sub>4</sub>, <em>X</em>, and <em>Y</em>.</p>","abstract_html":"&lt;p&gt;There are four orientations of cycles on four vertices. Necessary and sufficient conditions are given for covering complete directed digraphs &lt;em&gt;D&lt;sub&gt;v&lt;/sub&gt;&lt;/em&gt;, packing and covering complete bipartite digraphs, &lt;em&gt;D&lt;sub&gt;m,n&lt;/sub&gt;&lt;/em&gt;, and packing and covering the complete digraph on &lt;em&gt;v&lt;/em&gt; vertices with hole of size &lt;em&gt;w&lt;/em&gt;, &lt;em&gt;D&lt;/em&gt;(&lt;em&gt;v&lt;/em&gt;,&lt;em&gt;w&lt;/em&gt;), with three of the orientations of a 4-cycle, including &lt;em&gt;C&lt;/em&gt;&lt;sub&gt;4&lt;/sub&gt;, &lt;em&gt;X&lt;/em&gt;, and &lt;em&gt;Y&lt;/em&gt;.&lt;/p&gt;","abstract_has_math":false,"creators":["Cooper, Melody Elaine"],"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":2007,"date_issued":"2007-12-15T08:00:00Z","date_published":"2007-12-15T08:00:00Z","updated_at":"2026-07-24T02:21:19Z","subjects":["coverings","packings","design theory","graph theory","Discrete Mathematics and Combinatorics","Mathematics","Physical Sciences and Mathematics"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/2031","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Cooper, Melody Elaine"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2007-12-15T08:00:00Z"]},{"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":["coverings","packings","design theory","graph theory","Discrete Mathematics and Combinatorics","Mathematics","Physical Sciences and 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/3392/viewcontent/CooperM112507f.pdf","https://dc.etsu.edu/etd/2031"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>There are four orientations of cycles on four vertices. Necessary and sufficient conditions are given for covering complete directed digraphs <em>D<sub>v</sub></em>, packing and covering complete bipartite digraphs, <em>D<sub>m,n</sub></em>, and packing and covering the complete digraph on <em>v</em> vertices with hole of size <em>w</em>, <em>D</em>(<em>v</em>,<em>w</em>), with three of the orientations of a 4-cycle, including <em>C</em><sub>4</sub>, <em>X</em>, and <em>Y</em>.</p>"]},{"key":"dc:title","label":"Title","values":["Packings and Coverings of Various Complete Digraphs with the Orientations of a 4-Cycle."]}]}],"canonical_facts":{"dc:creator":["Cooper, Melody Elaine"],"dc:date.issued":["2007-12-15T08:00:00Z"],"dc:description.abstract":["<p>There are four orientations of cycles on four vertices. Necessary and sufficient conditions are given for covering complete directed digraphs <em>D<sub>v</sub></em>, packing and covering complete bipartite digraphs, <em>D<sub>m,n</sub></em>, and packing and covering the complete digraph on <em>v</em> vertices with hole of size <em>w</em>, <em>D</em>(<em>v</em>,<em>w</em>), with three of the orientations of a 4-cycle, including <em>C</em><sub>4</sub>, <em>X</em>, and <em>Y</em>.</p>"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/3392/viewcontent/CooperM112507f.pdf","https://dc.etsu.edu/etd/2031"],"dc:rights":["Copyright by the authors."],"dc:subject":["coverings","packings","design theory","graph theory","Discrete Mathematics and Combinatorics","Mathematics","Physical Sciences and Mathematics"],"dc:title":["Packings and Coverings of Various Complete Digraphs with the Orientations of a 4-Cycle."],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:21:19Z"}