Publication Date
2025
Presentation Length
20 minutes
College
College of Sciences & Mathematics
Department
Math and Computer Science, Department of
Student Level
Undergraduate
SPARK Category
Research
Faculty Advisor
Dr. Blake Dunshee
WELL Core Type
Intellectual Wellness
Metadata/Fulltext
Fulltext
SPARK Session
2:00-3:00 Topological Graph Theory
Presentation Type
Talk/Oral
Summary
In the spirit of Pisanski (1989) we consider orientable quadrilateral embeddings of Cartesian products of cycles on surfaces. We offer a constructive example of such an embedding of three low-order cycles. Then we show more generally that such embeddings exist for the product of a 2-cycle, and even cycle, and an arbitrary third cycle. We represent our graphs using rotation schemes to show this existence. Use of rotation schemes led to the ultimate characterization of our findings visually, providing conjectures for generalizations of products of three cycles.
Recommended Citation
Pisanski (1989) Ellingham, Liu, Ye, and Zha (2025+)
Included in
Discrete Mathematics and Combinatorics Commons, Geometry and Topology Commons, Set Theory Commons
