Many thanks to all the participants for their part in making the workshop a fruitful and enjoyable event. The next workshop in this series will take place in Domazlice, in the week preceding the Easter 2015 - that is,

AMarch 29-April 3, 2015.

Monday | ||

9:00 | Hajo Broersma | What's on the menu this week? (an appetizer) |

10:30 | Hao Li + Weihua Yang | Supereulerian graphs and hamiltonicity of line graphs |

14:30 | Zdenek Ryjacek | Stable forbidden subgraphs - what is behind? |

17:30 | Concert | |

Tuesday | ||

9:00 | Tomas Kaiser | The hypergraph proof technique - a tutorial |

14:30 | Petr Vrana | On 1-Hamilton-connectedness |

15:00 | Zdenek Ryjacek | Hourglasses, Hamilton-connectedness and 1-Hamilton-connectedness |

Wednesday | ||

9:00 | Kenta Ozeki | Tutte cycles and cycles of length linear of the order in line graphs |

11:00 | Shuya Chiba | Sets of cycles whose union dominates all edges |

13:45 | Excursion
to Klatovy
(more
catacombs)
(concert
programme) (concert
videos) | |

Thursday | ||

9:00 | Herbert Fleischner | Bipartizing matchings |

9:45 | C.-Q. Zhang | Nowhere-zero 3-flows |

10:30 | Edita Rollova | Nowhere zero flows in skew cartesian products |

14:30 | Arthur Hoffmann-Ostenhof | Nash-Williams Conjecture and the Dominating Cycle Conjecture (link to paper) |

The workshop was focused on problems and results related to the celebrated Matthews-Sumner Conjecture whose equivalent forms assert:

- Every 4-connected claw-free graph is hamiltonian. (Matthews, Sumner 1984)
- Every 4-connected line graph is hamiltonian. (Thomassen 1984)
- Every cyclically 4-edge-connected cubic graph has either a 3-edge-colouring or a dominating cycle. (Fleischner 1984)
- Every cyclically 4-edge-connected cubic graph has a dominating cycle. (Ash and Jackson 1989)

Topics within the scope of the workshop included:

- Hamiltonian properties of line graphs and claw-free graphs
- Forbidden induced subgraphs
- Closure operations, contractibility, collapsibility
- Graph toughness
- Cubic graphs, snarks
- Nowhere-zero flows and cycle covers

This event was the seventh in a series of workshops held in Nectiny (1999 and 2000), Hannover (2002), Hajek (2003) and Domazlice (2008, 2011).

**Domazlice**
is a charming town about 50 kms southwest of Pilsen
(see here
for some photos). The workshop began with dinner on March 24 and
ended with breakfast on March 29. It took place in the
hotel Sokolsky dum on the
main square of Domazlice (marked by a star
in this
map).

Accommodation was arranged in Sokolsky dum and in Penzion U Chodskeho hradu across the main square.

The following is the list of participants:

Yandong Bai | Hajo Broersma | Shuya Chiba | Evelyne Flandrin |

Weihua He | Arthur Hoffmann-Ostenhof | Hao Li | Kenta Ozeki |

Ingo Schiermeyer | Kiyoshi Yoshimoto | Weihua Wang | Cun-Quan Zhang |

...plus the organizers (Herbert Fleischner and Zdenek Ryjacek) and colleagues from the Pilsen group (Honza Brousek, Roman Cada, Honza Ekstein, Premek Holub, Tomas Kaiser, Roman Kuzel, Edita Rollova, Jakub Teska and Petr Vrana).

The workshop was co-organized by the Department of Mathematics at the University of West Bohemia in Pilsen. Support from the Institute for Theoretical Computer Science (CE-ITI) and the Union of Czech Mathematicians and Physicists (JCMF) is gratefully acknowledged.

The organizing committee was chaired by **Herbert Fleischner**
and **Zdenek Ryjacek**.

If you need additional information, please write to **ryjacek [@] kma
[.] zcu [.] cz**.