My first experience with suboptimal coloring was when I was about two years old. My mom got me one of those books with blank pictures of cartoon characters and I just scribbled all over the pages with red crayon. That’s pretty much what my latest paper is about. Here’s a PDF. The introduction is below, and continues after the jump. Some stuff in the paper is probably wrong, so let me know if you catch any mistakes.

**Computational Methods for Bounding Chromatic Numbers of Graphs**

**1 Introduction **

Many central problems in graph theory involve the process of graph coloring. A coloring of a graph is an assignment of a label, or “color,” to each vertex, such that no two connected vertices have the same color. Perhaps the most famous example is the problem of map coloring: a map determines a graph by assigning a node to each country, with an edge between two nodes whenever the corresponding countries share a border. A coloring of the graph then corresponds to a coloring of the map in which neighboring countries never share a color. Appel and Haken famously proved that for maps, there is always a coloring with no more than four colors [1]. Continue reading