This paper examines several polynomials related to the field of graph theory including the circuit partition polynomial, Tutte polynomial, and the interlace polynomial. We begin by explaining terminology and concepts that will be needed to understand the major results of the paper. Next, we focus on the circuit partition polynomial and its equivalent, the Martin polynomial. We examine the results of these polynomials and their application to the reconstruction of DNA sequences. Then we introduce the Tutte polynomial and its relation to the circuit partition polynomial. Finally, we discuss the interlace polynomial and its relationship to the Tutte and circuit partition polynomials.

Author Bio

I am currently a senior at Saint Michael㤼㸲s College. I am from Rutland, Vermont. I love to spend time with my family and two dogs, watch movies, and read. However, my passion is mathematics. This is why when I heard about the opportunity to work at Saint Michael’s for the summer conducting mathematical research I applied for the opportunity. During the semester I conducted preliminary research, and during the summer, worked full time. My main focus was to explore an area of graph theory that was related to DNA sequencing. Thus, I settled upon the circuit partition polynomial. Ultimately I wanted to explore as many aspects of the polynomial as closely as I could in the time allotted. The intended result of the research was to be able to produce a paper on the circuit partition polynomial that could be understood and appreciated by undergraduate mathematicians.