# Graphs and networks in context 2019

Summer program organized by Charles University and Zhejiang Normal University

**Dates:**June 24 – September 24 2019

**Place:**Charles University, Prague

## Tuturials by

- J. Nešetřil (Prague)
- J. Hubička (Prague)
- Lluís Vena Cros
- David Hartman (Prague)
- P. Ossona de Mendez (Paris, Prague)
- Z. Dvořák (Prague)
- R. Šámal (Prague)
- M. Konečný (Prague)
- A. Pultr (Prague)
- M. Loebl (Prague)

## Preliminary schedule

(Subject to changes.) The lectures, which are typically 90 minutes long, will take place at the building of Charles University, Malostranské náměstí, 25, Prague.Date | Time | Room | Speaker | Title |
---|---|---|---|---|

Week 1 | ||||

Tuesday, June 25 | 6:30 | Arrival, accomodation, registration | ||

Wednesday, June 26 | 9:00 | Meeting inside of metro station (take bus 177 from Otava) | ||

10:00–13:00 | Faculty headquaters, Ke karlovu 8 | Student IDs | ||

12:00 | Faculty headquaters, Ke karlovu 8 | Welcome by the dean of Charles University Jan Kratochvíl | ||

13:00–15:00 | S6 | Jaroslav Nešetřil | Ramsey thoerem (proof, Erdos 1947 bound). Lecture notes on Ramsey theorem | |

Thursday | 10:00–11:30 | S6 | Jaroslav Nešetřil | Ramsey theorem for hypergraphs, Shur theorem. Lecture notes on Shur theorem |

Friday, June 28 | 10:00–11:30 | S6 | Jaroslav Nešetřil | Ramsey theory: second proof of Shur theorem, infinite Ramsey theorem for graphs. Homework: Infinite Ramsey theorem for n-tuples |

13:00– | Guided tour to Prague | |||

Week 2 | ||||

Monday, July 1 | 10:00–11:30 | S6 | Jaroslav Nešetřil | Ramsey theory: existence of convex n-gons in large sets of points in general position. Compactness argument: infinite Ramsey theorem implies finite. Paris-Harrington theorem. |

Tuesday, July 2 | 10:00–11:30 | S6 | Jaroslav Nešetřil | Ramsey theory: van der Waerden and Hales Jewet theorems (no proofs). Structural Ramsey theory: abstract from of Ramsey theorem for structures. A-Ramsey property. Ramsey class. |

15:00–16:30 | S6 | Xuding Zhu | Fractional Hedetniemi’s conjecture | |

Wednesday, July 3 | 10:00–13:30 | S6 | Xuding Zhu | TBA |

13:30–17:00 | S6 | Seminar | ||

19:00–21:30 | National Theatre | Opera Tosca | ||

Thursday, July 3 | 10:00–13:30 | S6 | Problem session | |

Friday, July 5 | all day | state holiday | ||

Saturday, July 6 | all day | Trip to Karlštejn Castle | ||

Week 3 | ||||

Monday, July 8 | 10:00–12:00 | S6 | Jan Hubička | The Random graph. See also chapter by Peter Cameron |

Tuesday, July 9 | 10:00–12:00 | S6 | Jan Hubička | Random graph is homogeneous. Relational structures lecture notes |

19:00 | S5 | Oldřich Lipský, Jiří Brdečka | Limonadovy Joe | |

Wednesday, July 10 | 10:00–12:00 | S6 | Jan Hubička | Fraisse theorem |

Thursday, July 11 | 10:00–12:00 | S6 | Jan Hubička | Ramsey classes, EPPA |

Friday, July 12 | 10:00–12:00 | S6 | Martin Mareš | Generating graphs |

Week 4 | ||||

Monday, July 15 | 10:00–12:00 | S6 | Jaroslav Nešetřil | Structural Ramsey Theory: high chromatic graphs of large girth |

14:30 | Historical tram | |||

Tuesday, July 16 | 10:00–12:00 | S6 | Robert Šámal | Network flows |

14:00–15:30 | S6 | Michal Čertík | World bank | |

18:00–21:00 | S5 | Karel Zeman | Invention of Destruction | |

21:00–2:00 | Sky | Partial moon eclipse (best at 23:30) | ||

Wednesday, July 17 | 10:00–12:00 | S6 | Robert Šámal | Network flows |

Thursday, July 18 | 10:00–12:00 | S6 | Lluis Vena | Regularity lemma |

Friday, July 19 | 10:00–12:00 | S6 | Lluis Vena | Regularity lemma |

Week 5 | ||||

Monday, July 22-Friday 26 | Workshop and school on topological methods | |||

10:00–12:00 | S11 | Matěj Konečný | Introduction to computational complexity | |

Tusday, July 23 | all day | S5 | Topological methods tutorial | |

Wednesday, July 24 | 10:00–12:00 | S11 | Matěj Konečný | Introduction to computational complexity |

Thursday, July 25 | 10:00–12:00 | S11 | Pierre Simon | First order logic and 0/1 law of the Random graph |

14:00–16:00 | S11 | Patrice Ossona de Mendez | rank-width, linear rank-width and the tale of k-boundedness | |

Friday, July 26 | 10:00–12:00 | S11 | Pierre Simon | First order logic and 0/1 law of the Random graph |

Week 6 | ||||

Monday, July 19-Friday, August 2 | Midsummer Combinatorial Workshop XXIV | |||

Week 7 | ||||

Monday, August 5 | GDR | |||

Wednesday, August 7-Friday, August 9 | Trip to Český Krumlov, lectures by Jiří Fiala on topological minors | |||

Week 8 | ||||

Monday, August 12 | 10:00–12:00 | S6 | Tereza Vojtechova | Czech Legends |

afternoon | Tereza Vojtechova | Around Prague to places from legends (walk) | ||

Tuesday, August 13 | 10:00–12:00 | S6 | Tereza Vojtechova | The difference between Chinese, Moravian and Irish dance |

13:30-17:00 | S7 | Tereza Vojtechova | Irish Set dance worshop. Suitable shoes are important! You want to wear smooth-soled shoes which stay on your feet and don't slip off. No flip-flops or high-heeled shoes. | |

Friday, August 16 | 10:00–12:00 | S6 | Zdeněk Dvořák | Sublinear operators |

Week 9 | ||||

Saturday, August 17 | 8:30-19:30 | Trip to Czech Paradaise | ||

22:00-24:00 | Jazzdock: Terne Čhave | |||

Monday, August 19 | 10:00–12:00 | S6 | prof. Olga Lomová | China imagined by Europe |

Tuesday, August 20 | 10:00–12:00 | S6 | Andy Zucker | TBA |

14:00–16:00 | S6 | Andres Aranda | TBA | |

Wednesday, August 21 | 10:00–12:00 | S6 | Andres Aranda | TBA |

Thursday, August 22 | 9:00–12:00 | Visit to Strahov Monastery | ||

Week 10 | ||||

Tuesday, September 3 | 10:00–12:00 | S6 | Ales Pultr | Topology: general approach to continuity |

Wednesday, September 4 | 10:00–12:00 | S6 | Matrin Loebl | Edge cuts in planar graphs |