In this paper, we will contribute to research on a Graph Theory problem known as the Gold Grabbing Game. The game consists of two players and a tree in which each vertex has a positive integer value of gold. Players take turns removing leaves from the tree and deleting the associated edge until the graph is entirely empty. A winning condition is acquiring at least half of the total gold. Existing research shows that for a tree with an even number of vertices, Player 1 can always win.
It can also be shown via simple examples that for a tree with an odd number of vertices, the game board may favor Player 1 or Player 2, depending on the conguration of the tree, the integer values at a given vertex, or both. We will expand on the reason for Player 1's advantage on even trees and attempt to clarify the winning strategy, while also expanding on the case of an odd tree and various winning scenarios for Player 1 or 2.
","abstract_html":"<p>In this paper, we will contribute to research on a Graph Theory problem known as the Gold Grabbing Game. The game consists of two players and a tree in which each vertex has a positive integer value of gold. Players take turns removing leaves from the tree and deleting the associated edge until the graph is entirely empty. A winning condition is acquiring at least half of the total gold. Existing research shows that for a tree with an even number of vertices, Player 1 can always win.</p> <p>It can also be shown via simple examples that for a tree with an odd number of vertices, the game board may favor Player 1 or Player 2, depending on the conguration of the tree, the integer values at a given vertex, or both. We will expand on the reason for Player 1's advantage on even trees and attempt to clarify the winning strategy, while also expanding on the case of an odd tree and various winning scenarios for Player 1 or 2. </p>","abstract_has_math":false,"creators":["Acampa, Stephen"],"institution":"Eastern Kentucky University","degree_name":"Master of Science (MS)","degree_level":"Master's","degree_discipline":"Mathematics and Statistics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-01-01T08:00:00Z","date_published":"2018-01-01T08:00:00Z","updated_at":"2026-07-24T02:15:39Z","subjects":["Graph Theory","Mathematics"],"languages":[],"rights":["Copyright 2018 Stephen Acampa"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://encompass.eku.edu/etd/500","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Acampa, Stephen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Encompass Digital Archive, Eastern Kentucky University"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics and Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Eastern Kentucky University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Graph Theory","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 Stephen Acampa"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://encompass.eku.edu/etd/500"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this paper, we will contribute to research on a Graph Theory problem known as the Gold Grabbing Game. The game consists of two players and a tree in which each vertex has a positive integer value of gold. Players take turns removing leaves from the tree and deleting the associated edge until the graph is entirely empty. A winning condition is acquiring at least half of the total gold. Existing research shows that for a tree with an even number of vertices, Player 1 can always win.
It can also be shown via simple examples that for a tree with an odd number of vertices, the game board may favor Player 1 or Player 2, depending on the conguration of the tree, the integer values at a given vertex, or both. We will expand on the reason for Player 1's advantage on even trees and attempt to clarify the winning strategy, while also expanding on the case of an odd tree and various winning scenarios for Player 1 or 2.
"]},{"key":"dc:format","label":"Dc Format","values":["application/PDF"]},{"key":"dc:source","label":"Dc Source","values":["Encompass Digital Archive: Online Theses and Dissertations"]},{"key":"dc:title","label":"Title","values":["Results on the Gold Grabbing Game"]}]}],"canonical_facts":{"dc:creator":["Acampa, Stephen"],"dc:description.abstract":["In this paper, we will contribute to research on a Graph Theory problem known as the Gold Grabbing Game. The game consists of two players and a tree in which each vertex has a positive integer value of gold. Players take turns removing leaves from the tree and deleting the associated edge until the graph is entirely empty. A winning condition is acquiring at least half of the total gold. Existing research shows that for a tree with an even number of vertices, Player 1 can always win.
It can also be shown via simple examples that for a tree with an odd number of vertices, the game board may favor Player 1 or Player 2, depending on the conguration of the tree, the integer values at a given vertex, or both. We will expand on the reason for Player 1's advantage on even trees and attempt to clarify the winning strategy, while also expanding on the case of an odd tree and various winning scenarios for Player 1 or 2.
"],"dc:format":["application/PDF"],"dc:identifier":["https://encompass.eku.edu/etd/500"],"dc:publisher":["Encompass Digital Archive, Eastern Kentucky University"],"dc:rights":["Copyright 2018 Stephen Acampa"],"dc:source":["Encompass Digital Archive: Online Theses and Dissertations"],"dc:subject":["Graph Theory","Mathematics"],"dc:title":["Results on the Gold Grabbing Game"],"dc:type":["Master Thesis"],"thesis:degree_discipline":["Mathematics and Statistics"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Science (MS)"],"thesis:institution_name":["Eastern Kentucky University"]},"updated_at":"2026-07-24T02:15:39Z"}