Let H be a graph. G is a subgraph of H if V (G) ⊆ V (H) and E(G) ⊆ E(H). The subgraphs of H can be used to determine whether H is planar, a line graph, and to give information about the chromatic number. In a recent work by Beeler and Jamison [3], it was shown that it is difficult to obtain an automorphic decomposition of a triangle-free graph. As many of their examples involve circulant graphs, it is of particular interest to find triangle-free subgraphs within circulants. As a cycle with at least four vertices is a canonical example of a triangle-free subgraph, we concentrate our efforts on these. In this thesis, we will state necessary and sufficient conditions for the existence of edge induced and vertex induced cycles within circulants.
","abstract_html":"<p>Let <em>H</em> be a graph. <em>G</em> is a subgraph of <em>H</em> if <em>V</em> (<em>G</em>) ⊆ <em>V</em> (<em>H</em>) and <em>E</em>(<em>G</em>) ⊆ <em>E</em>(<em>H</em>). The subgraphs of <em>H</em> can be used to determine whether <em>H</em> is planar, a line graph, and to give information about the chromatic number. In a recent work by Beeler and Jamison [3], it was shown that it is difficult to obtain an automorphic decomposition of a triangle-free graph. As many of their examples involve circulant graphs, it is of particular interest to find triangle-free subgraphs within circulants. As a cycle with at least four vertices is a canonical example of a triangle-free subgraph, we concentrate our efforts on these. In this thesis, we will state necessary and sufficient conditions for the existence of edge induced and vertex induced cycles within circulants.</p>","abstract_has_math":false,"creators":["Wooten, Trina Marcella"],"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":2008,"date_issued":"2008-08-12T07:00:00Z","date_published":"2008-08-12T07:00:00Z","updated_at":"2026-07-24T02:21:11Z","subjects":["graph theory","circulants","subgraphs","cycles","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/1985","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Wooten, Trina Marcella"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2008-08-12T07:00:00Z"]},{"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","circulants","subgraphs","cycles","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/3337/viewcontent/WootenT072908f.PDF","https://dc.etsu.edu/etd/1985"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let H be a graph. G is a subgraph of H if V (G) ⊆ V (H) and E(G) ⊆ E(H). The subgraphs of H can be used to determine whether H is planar, a line graph, and to give information about the chromatic number. In a recent work by Beeler and Jamison [3], it was shown that it is difficult to obtain an automorphic decomposition of a triangle-free graph. As many of their examples involve circulant graphs, it is of particular interest to find triangle-free subgraphs within circulants. As a cycle with at least four vertices is a canonical example of a triangle-free subgraph, we concentrate our efforts on these. In this thesis, we will state necessary and sufficient conditions for the existence of edge induced and vertex induced cycles within circulants.
"]},{"key":"dc:title","label":"Title","values":["Finding Edge and Vertex Induced Cycles within Circulants."]}]}],"canonical_facts":{"dc:creator":["Wooten, Trina Marcella"],"dc:date.issued":["2008-08-12T07:00:00Z"],"dc:description.abstract":["Let H be a graph. G is a subgraph of H if V (G) ⊆ V (H) and E(G) ⊆ E(H). The subgraphs of H can be used to determine whether H is planar, a line graph, and to give information about the chromatic number. In a recent work by Beeler and Jamison [3], it was shown that it is difficult to obtain an automorphic decomposition of a triangle-free graph. As many of their examples involve circulant graphs, it is of particular interest to find triangle-free subgraphs within circulants. As a cycle with at least four vertices is a canonical example of a triangle-free subgraph, we concentrate our efforts on these. In this thesis, we will state necessary and sufficient conditions for the existence of edge induced and vertex induced cycles within circulants.
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/3337/viewcontent/WootenT072908f.PDF","https://dc.etsu.edu/etd/1985"],"dc:rights":["Copyright by the authors."],"dc:subject":["graph theory","circulants","subgraphs","cycles","Discrete Mathematics and Combinatorics","Mathematics","Physical Sciences and Mathematics"],"dc:title":["Finding Edge and Vertex Induced Cycles within Circulants."],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:21:11Z"}