8th Workshop on the Matthews-Sumner Conjecture and Related Problems

Pilsen, March 29-April 3, 2015

After the workshop

We thank all the participants for coming and for helping make the workshop an inspiring meeting with lots of new ideas and problems. The next workshop in the series will probably take place on April 9-14, 2017.

A photo gallery from this year's workshop is available.

The schedule of the workshop was as follows (links to slides are given where available):

Monday 30/3/2015
9:30		Opening (with a rememberance of Ralph Faudree)
9:40	Zdenek Ryjacek	The conjectures and around - A warm-up survey
10:30	Bill Jackson + Adthasit Sinna	Tutte trails in graphs on surfaces
14:30	Arthur Hoffmann Ostenhof	A survey on the 3-Decomposition Conjecture
16:00		Brewery tour
Tuesday
9:30	Roman Nedela	My favourite problems on snarks
10:15	Jiri Fiala	Hamiltonian properties and scattering number of interval graphs
10:45	Dan Kral	Two problems about cubic graphs
14:30	Tomas Kaiser	Hamilton cycles in essentially 9-connected line graphs
15:15	Kiyoshi Yoshimoto	On dominating even subgraphs in cubic graphs
19:00		Wine tasting
Wednesday
9:30	Akira Saito	The Ryjacek closure and a forbidden subgraph (plus a JCAA 2016 advertisement)
10:15	Hong-Jian Lai	Supereulerian graphs and hamiltonian line graphs
14:30	Liming Xiong	Singular edges and hamiltonicity in claw-free graphs with locally disconnected vertices
15:15	Ingo Schiermeyer	Hamiltonicity and forbidden induced subgraphs
19:00		Opera - Mascagni: Cavaleria rusticana, Leoncavallo: Pagliacci
Thursday
9:30	Weihua He	Hamilton cycles in spanning subgraphs of line graphs
10:15	Binlong Li	Heavy subgraph conditions for hamiltonian properties
14:30	Edita Rollova	Nowhere zero flows on signed series-parallel graphs
14:30	Kenta Ozeki	A HIST in cubic graphs
19:00		Dinner and farewell party

About the workshop

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 eighth in a series of workshops, previously held in Nectiny (1999 and 2000), Hannover (2002), Hajek (2003) and Domazlice (2008, 2011, 2013).

Location and dates

For the first time, the workshop took place in Pilsen, the 2015 European Capital of Culture. The workshop began with dinner on March 29 and ended with breakfast on April 3. The venue of the workshop was the comfortable Hotel Trend in the downtown of Pilsen yet in a relatively quiet street.

Participants

The following is the list of participants:

Yandong Bai	Jiri Fiala	Evelyne Flandrin	Weihua He
Arthur Hoffmann-Ostenhof	Bill Jackson	Dan Kral	Hong-Jian Lai
Hao Li	Roman Nedela	Kenta Ozeki	Akira Saito
Ingo Schiermeyer	Adthasit Sinna	Qiang Sun	Liming Xiong
Kiyoshi Yoshimoto

...plus the organisers (Herbert Fleischner and Zdenek Ryjacek) and colleagues from the Pilsen group (Honza Brousek, Roman Cada, Honza Ekstein, Premek Holub, Adam Kabela, Tomas Kaiser, Binlong Li, Martina Mockovciakova, Edita Rollova, Jakub Teska and Petr Vrana).

Organisers and contact

The workshop was co-organised by the Department of Mathematics at the University of West Bohemia in Pilsen and the Institute for Theoretical Computer Science (CE-ITI), with support from the Pilsen local chapter of the Union of Czech Mathematicians and Physicists. Partial support from project NEXLIZ (CZ.1.07/2.3.00/30.0038) is gratefully acknowledged.

The organising committee was chaired by Herbert Fleischner and Zdenek Ryjacek.

If you need additional information, please contact the organisers.