11th Workshop on the Matthews-Sumner Conjecture and Related Problems

Location and schedule

The workshop will take place on April 2-7, 2023 in Pilsen. The workshop starts with dinner on Sunday, April 2, 2023, and ends with breakfast on Friday, April 7, 2023. The venue of the workshop is the comfortable Hotel Trend in the downtown of Pilsen yet in a relatively quiet street (the same place as last time in 2019).

Programme

Breakfast is served each day between 7:30 and 9:00.

The main purpose of the workshop is to provide opportunity for informal meetings and discussions. The conference room (6th floor of the hotel) will be for this purpose equipped with dataprojector, blackboard and flipchart.

About the workshop

The upcoming event is the 11th in a series of workshops focused on the Matthews-Sumner Conjecture and related topics. The previous workshops took place in Nečtiny (1999 and 2000), Hannover (2002), Hájek (2003), Domažlice (2008, 2011, 2013) and Pilsen(2015, 2017,2019 ). The Matthews-Sumner Conjecture is interrelated with several other open problems in Graph Theory. For instance, some of the known equivalent formulations of this conjecture are the following:

• 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)

The topics of interest for the workshop include the following:

• hamiltonian properties of line graphs and claw-free graphs,
• uniquely hamiltonian graphs,
• forbidden induced subgraphs,
• closure operations, contractibility, collapsibility,
• graph toughness,
• cubic graphs, snarks,
• nowhere-zero flows and cycle covers.

As usual, there will be talks presenting new progress in the field, and we would like to keep enough time for individual discussions and working in small groups.

Participants

The following colleagues already confirmed participation:

plus of course the organizers and the Pilsen group.

Workshop fee

The workshop is by invitation only and there is no workshop fee.

Travel information

Pilsen is located near the D5 motorway from Prague to Germany. Connections by public transport between Prague and Pilsen are frequent and convenient. To check for public transport connections, use this page (it has English and German versions). If you need assistance, please ask the organisers.

When coming from Prague airport, there are two options:

• The simpler one is to take the Airport Express (AE) bus to the main train station (Hlavní nádraží) and take the train to Pilsen from there.
• The faster option is to take the 100 bus to Zličín subway terminal, and then take the yellow RegioJet bus to Pilsen. It is advisable (and in peak times such as Sunday afternoon, absolutely necessary) to make an advance booking for the RegioJet bus.

The AE and the 100 bus run at least twice an hour. When searching for connections using the above page, enter "Praha Terminal 1" (or 2) as the point of departure.

Once in Pilsen, it may be best to take a taxi, although the hotel is just a 10 minute eastward walk away from the bus station (see the map).

Organisers and contact

The organising committee is chaired by Herbert Fleischner and Zdeněk Ryjáček. For additional information about the workshop, please contact Přemek Holub or Mária Skyvová.

The event is co-organised by the Department of Mathematics of the Faculty of Applied Sciences.

The workshop is partly supported by project GA20-09525S of the Czech Science Foundation.