#### Year of Publication

2005

#### Date of Thesis

05-2005

#### Document Type

Thesis

#### Department

Mathematics

#### Abstract

Using the deletion contraction algorithm we can find the chromatic polynomials for graphs. Similar to combinatorial proofs, we can apply this algorithm in different ways to the same graph to derive polynomial identities. Also, we will be looking at a couple of results from a previous paper and provide alternate proofs. Lastly, we will give a formula for the chromatic polynomial of an Apple Tree. Roughly, an Apple Tree is a tree with cycles attached at its vertices.

#### Recommended Citation

Tang, Donny, "Deletion and Contraction Games: Chromatic Polynomial Proofs and Making Sense of an Apple Tree" (2005). *Mathematics Honors Theses*. 10.

http://digitalcommons.ithaca.edu/math_honors_theses/10