## Fractional Hedetniemi’s conjecture and Chromatic Ramsey number – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Title: Fractional Hedetniemi’s conjecture and Chromatic Ramsey number

Lecturer: Xuding Zhu

Date: November 9, 2016

Main Topics: Chromatic Ramsey numbers, lower bound for them, Hedetniemi’s conjecture, fractional Hedetniemi’s conjecture.

Definitions: $\rho$-Ramsey number, $\chi$-Ramsey number, wreath product, product graph, graph homomorphism, fractional chromatic number

## Bootcamp 4 – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Special thanks to Matěj Konečný for helpful feedback.

Title: Bootcamp 4 (of 8)

Lecturer: Jaroslav Nešetřil

Date: Monday September 26, 2016.

Main Topics: Graphs have the ordering property, Ordered Edge-Ramsey implies Ordering property, Graphs are not Ramsey, Amalgamation for Ramsey classes, the product argument, Hilbert’s Theorem.

Definitions: Joint Embedding Property, Amalgamation Property, statement of Hilbert’s Theorem.

Bootcamp 1 – Bootcamp 2 – Bootcamp 3 – Bootcamp 4 – Bootcamp 5Bootcamp 6Bootcamp 7 – Bootcamp 8