[This is just a placeholder for the moment. I’ll update it a bit more later.]

# Tag: graph theory

## 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:** -Ramsey number, -Ramsey number, wreath product, product graph, graph homomorphism, fractional chromatic number

## Hrushovski constructions – 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**: Hrushovski constructions 1 (of 3)

**Lecturer**: David Evans

**Date**: November 7, 2016

**Main Topics**: Definition Review, -very-sparse iff -orientable, Existence of graph without Ramsey expansion.

**Definitions:** -very-sparse, -orientable,

Continue reading Hrushovski constructions – Ramsey DocCourse Prague 2016

## Dynamical systems and Ramsey theory – 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**: Ergodic theory and amenable groups

**Lecturer**: Benjamin Weiss

**Date**: October 31, 2016.

**Main Topics**: Three equivalent notions of amenability, Basic concepts in ergodic actions, Furstenberg’s Ergodic proof of Szemerédi’s theorem

**Definitions:** Ergodic action, weak mixing, mixing, Banach limit, amenable group, left invariant mean, paradoxical decomposition, Følner sequence

Continue reading Dynamical systems and Ramsey theory – Ramsey DocCourse Prague 2016

## Functions on Homogeneous Ramsey Structures 3 – Ramsey DocCourse Prague 2016

**Title**: Functions on Homogeneous Ramsey Structures 3 (of 3).

**Lecturer**: Michael Pinsker.

**Date**: Friday October 14, 2016.

**Main Topics**: Proof of Ramsey claim for canonical functions, Thomas’ Theorem for the Rado Graph, Open questions

**Definitions:** No new definitions

Lecture 1 – Lecture 2 – Lecture 3

Continue reading Functions on Homogeneous Ramsey Structures 3 – Ramsey DocCourse Prague 2016

## Bootcamp 6 – Ramsey DocCourse Prague 2016

**Title**: Bootcamp (6 of 6)

**Lecturer**: Jaroslav Nesetril

**Date**: Monday October 3, 2016.

**Main Topics**: Other applications of the “product argument”, Chain-Ramsey for Posets, Proof of edge-Ramsey for Graphs, Proof of Hales-Jewett

**Definitions:** Structural pigeonhole principle, Poset, Graph product, Combinatorial line

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

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## Bootcamp 3 – Ramsey DocCourse Prague 2016

**Title**: Bootcamp (3 of 6)

**Lecturer**: Jaroslav Nešetřil

**Date**: Friday September 23, 2016.

**Main Topics**: Point Ramsey for graphs, hypergraphs.

**Definitions:** Ramsey property for finite structures, Ramsey Class, point-Ramsey, edge-Ramsey, hypergraphs, Chromatic number, Ordering Property.

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