**Title: **Graph Embeddings and Map Colorings

Speaker: |
Jason Gao |

Affiliation: |
Carleton University |

Location: |
MC 5501 |

**Abstract: **The famous Map Color Theorem says that the chromatic number of a surface of Euler characteristic $c<0$ is equal to $\displaystyle \left\lfloor \frac{1}{2}\left(7+\sqrt{49-24c}\right)\right\rfloor $. This was proved in 1969 by Ringel and Youngs who showed that $K_n$ can be embedded on surfaces of Euler characteristic $c$ such that $\displaystyle n= \left\lfloor \frac{1}{2}\left(7+\sqrt{49-24c}\right)\right\rfloor $. This leads to the study about the genus distribution of a graph $G$, that is, the number of embeddings of $G$ on surfaces. This talk will go through some recent results about genus distributions of bouquets and cubic graphs. Some results and conjectures will also be given about the distribution of the chromatic number of a random map on a given surface.