A Whirlwind Tour of Fractional Graph Theory
The four-color theorem is notoriously difficult to prove, while the five-color theorem has a relatively simple proof. What about the four-and-a-half color theorem? Would this be easy to prove, or hard? What does it even mean to color a graph with four-and-a-half colors? We'll investigate this kind of question as applied to a variety of graph theory parameters that are usually whole numbers but that we attempt to extend to real or rational values. In addition to the chromatic number, such parameters include the matching number, the packing number, the covering number, the domination number, the clique number, the intersection number, and even the genus.
This talk is recommended for undergrads.