Results on the Gold Grabbing Game

<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>

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Master's

Discipline thesis:degree_discipline

Mathematics and Statistics

Grantor dc:publisher

Eastern Kentucky University

Year

2018

Author dc:creator

• Acampa, Stephen

• Graph Theory
• Mathematics

Statement dc:rights

• Copyright 2018 Stephen Acampa

Repository record dc:identifier

https://encompass.eku.edu/etd/500

OAI identifier oai:identifier

oai:encompass.eku.edu:etd-1498