Date of Submission

Spring 2012

Academic Program

Mathematics

Project Advisor 1

Ethan Bloch

Project Advisor 2

Maria Belk

Abstract/Artist's Statement

Study of the Sprouts Game End Graphs

Sprouts is a pencil-and-paper game with interesting mathematical properties. In the version of the game that I am studying, this two-person game begins with n points on a piece of paper. A move is drawing a line joining two points or a point to itself, and then adding a new point on the line, subject to the conditions which the line does not cross another line, and the degree of each point does not exceed three. In this project, I was motivated by the question of characterizing the cubic graphs that can be obtained by Sprouts and ended up that I investigated some different cases of Sprouts end graphs. I have thus far attempted to prove the counter example raised in the paper by T.K.Lam that cannot be got from Sprouts game, which may be the first step to finding the other cubic graphs resulting from the Sprouts game. Also, I showed and proved some particular graphs that can or cannot be obtained by Sprouts.

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