Center for                           Nonlinear Analysis
CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact

## 2017 Summer Undergraduate Applied Mathematics Institute

### Projects:

• The Impact of three point differential on winning in the national basketball association, Yu Pan
Abstract:  For a graph $G$ with $m$ vertices, $\frac{M(G,n)}{\left(\frac{\binom{n}{m}m!}{|Aut(G)|}\right)}$ is called the $\textbf{density}$ or $\textit{Ramsey multiplicity constant}$ and is denoted by $C(G,n)$. Burr and Rosta proved that $C(G,n)$ is nondecreasing in $n$, stated that $G$ is $\textit{common}$ if $\displaystyle{\lim_{n \to \infty} C(G,n) = 2^{1-e}}$, and Jagger showed that any graph containing $K_4$ is non-common. This paper discusses the maximum of rainbow subgraphs in $K_n$ of certain graphs (i.e. disjoint stars, complete graphs, bipartite graphs).