Student: | Karel Král |
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Office: | 450 |

School: | Charles University in Prague |

E-mail: | kralka guess_what_is_here kam.mff.cuni.cz |

Project: | Ramsey Theory for Graphs with Ordered Vertices |

Next Project: | DIMACS REU 2014 |

Let S=([n], E) be an undirected graph where the vertex set is {1,2,3, ..., n} and E is a set of unordered tuples of vertices. We will ask Ramsey type questions involving ordering of vertices.

We work on estimates of Ramsey numbers for various graphs for example stars and paths with given permutation of verticies.

- Fox, Pach, Sudakov, Suk: Erdos-Szekeres-type theorems for Monotone Paths and Convex Bodies
- Milans, Stolee, West: Ordered Ramsey Theory and Track Representations of graphs
- Moshkovitz, Shapira: Ramsey Theory Integer Partitions and New Proof of the Erdos Szekeres Theorem

- We know that there are constant differences between Ramsey numbers for some permutations of graphs. There might be even assymptotic differences.
- We almost finished notes on discrepancy theory presented by Raghu Meka.
- Working on proof from Bridge Workshop (Bulgarian Solitaire).

http://www.mgvis.com/

http://www.mgvis.com/AbelloVitaResearchOct08.html