https://orcid.org/0000-0002-5223-9748
Abstract
The Game of Cycles, introduced by Su in 2020, is played on a simple connected planar graph together with its bounded cells, and players take turns marking edges with arrows according to a sink-source rule that gives the game a topological flavor. The object of the game is to produce a cycle cell—a cell surrounded by arrows all cycling in one direction—or to make the last possible move. We analyze the two-player game for various classes of graphs and determine who has a winning strategy. We also establish a topological property of the game: that a board with every edge marked must have a cycle cell.
Acknowledgments
The authors wish to thank The American Institute of Mathematics (AIM) and The Institute for Computational and Experimental Research in Mathematics (ICERM) for bringing us together at the 2019 Research Experiences for Undergraduate Faculty program, which was made possible by the support from the National Science Foundation (NSF) through Grants NSF-DMS 1620073 to AIM and NSF-DMS 1620080 to ICERM. Finally, the authors would like to thank Amit Harlev and the anonymous referees and editors for carefully reading the manuscript and providing helpful suggestions.
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Notes on contributors
Ryan Alvarado
RYAN ALVARADO received his Ph.D. in mathematics from the University of Missouri-Columbia in 2015. After spending three years at the University of Pittsburgh as a post-doctoral research fellow, he joined the faculty at Amherst College where he continues to carry out his research and teaching in mathematics, and to fulfill his commitment to increasing access to STEM majors among all underrepresented groups. Department of Mathematics and Statistics, Amherst College, Amherst, MA 01002, USA rjalvarado@amherst.edu
Maia Averett
MAIA AVERETT joined the faculty at Mills College in 2008 after earning her Ph.D. in mathematics from the University of California, San Diego. She is an active advocate for underrepresented groups in mathematics and finds value in projects that increase mathematical accessibility. Department of Mathematics and Computer Science, Mills College, Oakland, CA 94613, USA maverett@mills.edu
Benjamin Gaines
BENJAMIN GAINES received his Ph.D. in mathematics from Duke University in 2015. After receiving his Ph.D., he joined the faculty at Iona College. Aside from combinatorial games, his interests include using writing in teaching mathematics, and how to best provide effective student support. Department of Mathematics and Physics, Iona College, New Rochelle, NY 10801, USA bgaines@iona.edu
Christopher Jackson
CHRISTOPHER JACKSON works in the education department in the Coleman federal prison in Florida. He enjoys reading about ideas in analysis and number theory. His hobbies include studying, reading, working out, and keeping current with world events. FCI Coleman Low, Federal Correctional Institution, P.O. Box 1031 Coleman, FL 33521
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. Department of Mathematics and Computer Science, Providence College, Providence, RI 02918, USA mkarker@providence.edu
Malgorzata Aneta Marciniak
MALGORZATA ANETA MARCINIAK received her Ph.D. from Missouri University of Science and Technology and after joining CUNY, she became interested in mentoring students’ research projects. She is involved in improving her mentoring skills by studying theories of creativity and in searching for new projects topics. LaGuardia Community College of the City University of New York, Long Island City, NY 11101, USA mmarciniak@lagcc.cuny.edu
Francis Su
FRANCIS SU enjoys thinking about problems with a combinatorial and topological flavor. He earned his Ph.D. at Harvard and joined the faculty at Harvey Mudd College in 1996. From 2015 to 2017, he served as MAA President. His 2020 book Mathematics for Human Flourishing is an inclusive vision of what math is, who it’s for, and why anyone should learn it. Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA su@math.hmc.edu
Shanise Walker
SHANISE WALKER received her Ph.D. in Mathematics from Iowa State University in 2018. After receiving her Ph.D., she joined the faculty at the University of Wisconsin-Eau Claire, where she is active in research, teaching, and service to the mathematical profession related to equity, diversity, and inclusion. Department of Mathematics, University of Wisconsin-Eau Claire, Eau Claire, WI 54701, USA walkersg@uwec.edu