On Finite Collections of 4-Connected Graphs Generated By Forbidden Triples That Contain a Star

Date of Award

12-1-2023

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

First Advisor

Agnes D. Garciano, PhDReginaldo M. Marcelo, PhD

Abstract

I would like to express my deepest gratitude and appreciation to the following who have contributed to the completion of this dissertation. Their guidance, support, and encouragement have been invaluable throughout this journey.

First and foremost, I am immensely grateful to my advisers, Dr. Agnes D. Garciano and Dr. Reginaldo M. Marcelo, for their unwavering commitment, expertise, and patience. Their guidance and insightful feedback have been instrumental in shaping the direction and quality of this research. I am truly fortunate to have had their mentorship and support throughout this research.

To my panel members, Dr. Arnold A. Eniego, Dr. Yvette Lim, Dr. Felix P. Muga II and Dr. Mark Anthony Tolentino. Their valuable input, constructive criticism, and thorough review of my work have significantly enhanced the rigor and depth of this research. I am grateful for their time, expertise, and willingness to share their knowledge.

To Professor Yoshimi Egawa and Professor Keiko Kotani for the dissertation problem and for their helpful comments.

To all my professors in the Mathematics Department of AdMU, whose teachings, expertise, dedication and seminars have expanded my understanding and enriched my academic growth and experience.

To CHED, for providing financial support and the necessary funding for my studies.

To AdDU, for the support.

To my family and friends, for their unwavering support and prayers.

To the Almighty God, for the grace and mercy that make me overcome the challenges in this journey.

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