The goal of this thesis is to explore the topic of graph coloring and expand on existing ideas in the field of Graph Theory. These developments will then be used to provide a possible approach in proving the 4 – color theorem that was made famous by Guthrie in the 1800’s.
Since the theorem was presented, many proofs were presented and eventually disregarded for one reason or another. Today, the types of proofs that are considered correct all rely on a computer. The first of this kind was set forth by Appel and Haken in 1977. The driving idea behind their proof was exhaustive analysis. A different approach will be taken here.
The 4 – color theorem stated is: “Any finite, planar graph can be colored using 4 (at most) colors in such a manner that no adjacent vertices will share the same color.” While a complete proof of the theorem may not be possible to complete in this thesis, an intuitive idea will be presented that has potential to be expanded on in the future.
","abstract_html":"<p>The goal of this thesis is to explore the topic of graph coloring and expand on existing ideas in the field of Graph Theory. These developments will then be used to provide a possible approach in proving the 4 – color theorem that was made famous by Guthrie in the 1800’s.</p> <p>Since the theorem was presented, many proofs were presented and eventually disregarded for one reason or another. Today, the types of proofs that are considered correct all rely on a computer. The first of this kind was set forth by Appel and Haken in 1977. The driving idea behind their proof was exhaustive analysis. A different approach will be taken here.</p> <p>The 4 – color theorem stated is: “Any finite, planar graph can be colored using 4 (at most) colors in such a manner that no adjacent vertices will share the same color.” While a complete proof of the theorem may not be possible to complete in this thesis, an intuitive idea will be presented that has potential to be expanded on in the future.</p>","abstract_has_math":false,"creators":["Brady, Matthew"],"institution":null,"degree_name":"Master of Science","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["J. Christopher Tweddle, Ph.D.","Andrius Tamulis, Ph.D.","Jing Zhang, Ph.D."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-10-01T07:00:00Z","date_published":"2016-10-01T07:00:00Z","updated_at":"2026-07-24T02:24:36Z","subjects":["4 – color theorem","graph coloring","graph theory","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opus.govst.edu/theses/87","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["J. Christopher Tweddle, Ph.D.","Andrius Tamulis, Ph.D.","Jing Zhang, Ph.D."]},{"key":"dc:creator","label":"Author","values":["Brady, Matthew"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2017-01-26T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["4 – color theorem","graph coloring","graph theory","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://opus.govst.edu/theses/87"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The goal of this thesis is to explore the topic of graph coloring and expand on existing ideas in the field of Graph Theory. These developments will then be used to provide a possible approach in proving the 4 – color theorem that was made famous by Guthrie in the 1800’s.
Since the theorem was presented, many proofs were presented and eventually disregarded for one reason or another. Today, the types of proofs that are considered correct all rely on a computer. The first of this kind was set forth by Appel and Haken in 1977. The driving idea behind their proof was exhaustive analysis. A different approach will be taken here.
The 4 – color theorem stated is: “Any finite, planar graph can be colored using 4 (at most) colors in such a manner that no adjacent vertices will share the same color.” While a complete proof of the theorem may not be possible to complete in this thesis, an intuitive idea will be presented that has potential to be expanded on in the future.
"]},{"key":"dc:title","label":"Title","values":["The Four Color Theorem: A Possible New Approach"]}]}],"canonical_facts":{"dc:contributor":["J. Christopher Tweddle, Ph.D.","Andrius Tamulis, Ph.D.","Jing Zhang, Ph.D."],"dc:creator":["Brady, Matthew"],"dc:date.available":["2017-01-26T08:00:00Z"],"dc:description.abstract":["The goal of this thesis is to explore the topic of graph coloring and expand on existing ideas in the field of Graph Theory. These developments will then be used to provide a possible approach in proving the 4 – color theorem that was made famous by Guthrie in the 1800’s.
Since the theorem was presented, many proofs were presented and eventually disregarded for one reason or another. Today, the types of proofs that are considered correct all rely on a computer. The first of this kind was set forth by Appel and Haken in 1977. The driving idea behind their proof was exhaustive analysis. A different approach will be taken here.
The 4 – color theorem stated is: “Any finite, planar graph can be colored using 4 (at most) colors in such a manner that no adjacent vertices will share the same color.” While a complete proof of the theorem may not be possible to complete in this thesis, an intuitive idea will be presented that has potential to be expanded on in the future.
"],"dc:identifier":["https://opus.govst.edu/theses/87"],"dc:subject":["4 – color theorem","graph coloring","graph theory","Mathematics"],"dc:title":["The Four Color Theorem: A Possible New Approach"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science"]},"updated_at":"2026-07-24T02:24:36Z"}