Summary
The Game of Cycles is a two-player impartial mathematical game, introduced by Francis Su in his book Mathematics for Human Flourishing (2020). The game is played on simple planar graphs in which players take turns marking edges using a sink-source rule. In Alvarado et al., the authors determine who is able to win on graphs with certain types of symmetry using a mirror-reverse strategy. In this paper, we analyze the game for specific types of cactus graphs using a modified version of the mirror-reverse strategy.
Acknowledgments
We extend our gratitude to Jonah Amundsen and to Peter Graziano, doctoral student at the University of Connecticut, for their assistance with early aspects of the project. The authors would like to thank the reviewers for their comments. We also thank the University of Wisconsin-Eau Claire Department of Mathematics, the Office of Research and Sponsored Projects for supporting Jonah Amundsen, Heather Baranek, and Shanise Walker on this project. In addition, we also thank the University of Wisconsin-Eau Claire Foundation, Walter M. Reid First Year Research Fellowship, and the Blugold Fellowship for supporting Heather Baranek. Most of the work for this project was completed while Samuel Adefiyiju and Alison LaBarre were students at Providence College.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Notes on contributors
Samuel Adefiyiju
SAMUEL ADEFIYIJU is a Software Engineer at Raytheon Missiles and Defense who graduated Summa Cum Laude from Providence College with a bachelor’s degree in Computer Science and a minor in Mathematics. His interests are software development, cybersecurity, algorithm optimization, and database management.
Heather Baranek
HEATHER BARANEK received her Bachelor of Science degree in Software Engineering and Statistics from the University of Wisconsin-Eau Claire in 2022. As an undergraduate, she joined the Game of Cycles research team due to her interest in graph theory and its applicability in computer science.
Abigail Daly
ABIGAIL DALY graduated from Providence College in 2023, where she received her degree in Computer Science with a minor in Mathematics. She was drawn to the project after hearing a lecture about game theory in her discrete math class.
Xadia Goncalves
XADIA M. GONCALVES graduated from Providence College in 2022, where she received her degree in Biology with a Spanish minor. While at Providence College, she worked on an independent research project that focused on predator-prey interactions. Xadia is a Western University of Health Sciences Summer Health Professions Education Program (SHPEP) alumna.
Mary Leah Karker
MARY LEAH KARKER received her Ph.D. in mathematics from Wesleyan University in 2016. She held a visiting position at Connecticut College for two years before joining the faculty at Providence College where she enjoys teaching a variety of undergraduate courses and mentoring students in research. While she loves exploring new areas of mathematics, her primary research interests are in mathematical logic and foundations.
Alison Labarre
ALISON LABARRE received her Bachelor of Arts in mathematics with a minor in computer science from Providence College. After graduating she was offered a job at Newgrange Design, where she is in the process of becoming a printed circuit board designer.
Shanise Walker
SHANISE WALKER is an Assistant Professor of Mathematics at Clark Atlanta University. She received her Ph.D. in Mathematics from Iowa State University in 2018. Her research interests lie in combinatorics and graph theory. She has supervised several undergraduate research projects. Walker is active in service to the mathematical profession related to equity, diversity, inclusion, and belonging.