Caterpillar, Lobster, X graphs

Authors

Gerald Melin, College of Saint Benedict/Saint John's UniversityFollow
Landon Seward, College of Saint Benedict and Saint John's UniversityFollow
Will Mahowald, College of Saint Benedict/Saint John's UniversityFollow
Xavier Jones, College of Saint Benedict/Saint John's UniversityFollow

Document Type

Poster

Publication Date

4-25-2024

Disciplines

Mathematics

Advisor

Bret Benesh

Abstract

We studied a combinatorial game played between two players ("Alpha", who goes first, and "Beta", who goes second). The idea is that there are a lot of lightbulbs in a large warehouse, and they take turns turning a light bulb on. When a light bulb is turned on, it illuminates the area directly by it as well as the areas immediately surrounding it. The player who is the one to make all of the warehouse illuminated is the winner. This can be modeled on a graph. The two players take turns (1) selecting a vertex that has not yet been illuminated (and (2) coloring that vertex and its immediate neighbors. The last player to move wins. We can vary the game by changing the graph are we playing on. We have been working on this problem all semester, and we will be present on our partial results.

Recommended Citation

Melin, Gerald; Seward, Landon; Mahowald, Will; and Jones, Xavier, "Caterpillar, Lobster, X graphs" (2024). Celebrating Scholarship and Creativity Day (2018-). 239.
https://digitalcommons.csbsju.edu/ur_cscday/239