# Graph Ramsey theory

January 26 to January 30, 2015

at the

American Institute of Mathematics, San Jose, California

organized by

David Conlon, Jacob Fox, and Dhruv Mubayi

## Original Announcement

This workshop will be devoted to graph Ramsey theory. The Ramsey number of a graph $H$, denoted $r(H)$, is the smallest $n$ such that any two-coloring of the edges of the complete graph on $n$ vertices is guaranteed to contain a monochromatic copy of $H$. That these numbers exist was first proved by Ramsey in 1930. Since the 1970s, a coherent theory has grown around estimating these numbers and their many variants. In this workshop, we intend to study some topics which have proved particularly fruitful in recent years.

The main topics for the workshop are:

• Hypergraph Ramsey numbers
• Generalized Ramsey numbers
• Geometric Ramsey theorems

## Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A problem list compiled by Yufei Zhao.

Papers arising from the workshop:

Constructions in Ramsey theory
by  Dhruv Mubayi and Andrew Suk
Off-diagonal hypergraph Ramsey numbers
by  Dhruv Mubayi and Andrew Suk,  J. Combin. Theory Ser. B 125 (2017), 168–177  MR3641804
On the Erdős-Hajnal conjecture for six-vertex tournaments
by  Eli Berger, Krzysztof Choromanski and Maria Chudnovsky
Ramsey numbers of degenerate graphs
by  Choongbum Lee
Hedgehogs are not color blind
by  David Conlon, Jacob Fox and Vojtech Rodl
Hypergraph Ramsey numbers: tight cycles versus cliques
by  Dhruv Mubayi and Vojtech Rodl,  Bull. Lond. Math. Soc. 48 (2016), no. 1, 127-134  MR3455756