William Overman, Some Ordered Ramsey Numbers of Graphs on Four Vertices

Ordered Ramsey numbers were introduced in 2014 by Conlon, Fox, Lee, and Sudakov. Their results included upper bounds for general graphs and lower bounds showing separation from classical Ramsey numbers. We show the first nontrivial results for ordered Ramsey numbers of specific small graphs. In particular we prove upper bounds for orderings of graphs on four vertices, and determine some numbers exactly using  SAT solvers for lower bounds. These results are in the spirit of exact calculations for classical Ramsey numbers and use only elementary combinatorial arguments.

This is joint work with Jeremy Alm, Kayla Coffey, and Carolyn Langhoff.