In a paper by Beeler and Hoilman, the traditional game of peg solitaire is generalized to graphs in the combinatorial sense. One of the important open problems in this paper was to classify solvable trees. In this thesis, we will give necessary and sufficient conditions for the solvability for all trees with diameter four. We also give the maximum number of pegs that can be left on such a graph under the restriction that we jump whenever possible.
","abstract_html":"<p>In a paper by Beeler and Hoilman, the traditional game of peg solitaire is generalized to graphs in the combinatorial sense. One of the important open problems in this paper was to classify solvable trees. In this thesis, we will give necessary and sufficient conditions for the solvability for all trees with diameter four. We also give the maximum number of pegs that can be left on such a graph under the restriction that we jump whenever possible.</p>","abstract_has_math":false,"creators":["Walvoort, Clayton A"],"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":"2013-05-01T07:00:00Z","date_published":"2013-05-01T07:00:00Z","updated_at":"2026-07-24T02:19:59Z","subjects":["graph theory","peg solitaire","games on graphs","combinatorial games","Discrete Mathematics and Combinatorics"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/1113","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Walvoort, Clayton A"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-03-29T07:00:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2013-05-01T07:00:00Z"]},{"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","peg solitaire","games on graphs","combinatorial games","Discrete Mathematics and Combinatorics"]}]},{"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/2286/viewcontent/WalvoortC040413f.pdf","https://dc.etsu.edu/etd/1113"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In a paper by Beeler and Hoilman, the traditional game of peg solitaire is generalized to graphs in the combinatorial sense. One of the important open problems in this paper was to classify solvable trees. In this thesis, we will give necessary and sufficient conditions for the solvability for all trees with diameter four. We also give the maximum number of pegs that can be left on such a graph under the restriction that we jump whenever possible.
"]},{"key":"dc:title","label":"Title","values":["Peg Solitaire on Trees with Diameter Four"]}]}],"canonical_facts":{"dc:creator":["Walvoort, Clayton A"],"dc:date.available":["2013-03-29T07:00:00Z"],"dc:date.issued":["2013-05-01T07:00:00Z"],"dc:description.abstract":["In a paper by Beeler and Hoilman, the traditional game of peg solitaire is generalized to graphs in the combinatorial sense. One of the important open problems in this paper was to classify solvable trees. In this thesis, we will give necessary and sufficient conditions for the solvability for all trees with diameter four. We also give the maximum number of pegs that can be left on such a graph under the restriction that we jump whenever possible.
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/2286/viewcontent/WalvoortC040413f.pdf","https://dc.etsu.edu/etd/1113"],"dc:rights":["Copyright by the authors."],"dc:subject":["graph theory","peg solitaire","games on graphs","combinatorial games","Discrete Mathematics and Combinatorics"],"dc:title":["Peg Solitaire on Trees with Diameter Four"],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:19:59Z"}