On April 13, 2021, William Overman from the University of California, Irvine and the IBS Discrete Mathematics Group gave a talk on the ordered Ramsey numbers of small graphs at the Discrete Math Seminar. The title of his talk was “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.
The IBS discrete mathematics group welcomes two new students.
Donggyu Kim (김동규) is a new graduate student from July 2019 and is currently a graduate student at the department of mathematical sciences, KAIST.
William Overman is a visiting student from June 2019 to August 2019 and is currently an undergraduate student in California Institute of Technology. His research visit is sponsored by his home university.