10th Workshop on the Matthews-Sumner Conjecture and Related Problems

Location and schedule

The workshop will take place on April 14-19, 2019 in Pilsen. The workshop starts with dinner on Sunday, April 14, 2019, and ends with breakfast on Friday, April 19, 2019. 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 2017).

Programme

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

About the workshop

The upcoming event is the tenth 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 and 2013) and Pilsen(2015, 2017). 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 fee, which covers all local expenses, is 9000 Kc (Czech crowns - with the current exchange rates, this equals approx. 360 EUR, or 410 USD); reduced fee (without accommodation) is 4000 Kc (160 EUR, 185 USD). Unfortunately, unlike in the last years, we cannot offer a similarly generous programme for supporting local expenses as last time. However, if you are deeply interested, and have problems with funding, let us know, we will try. However, we cannot support travel costs.

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 Nedelová

The event is co-organised by the Department of Mathematics of the Faculty of Applied Sciences, University of West Bohemia in Pilsen, and the Pilsen branch of the Institute for Theoretical Computer Science (CE-ITI), with the support of the Pilsen branch of the Union of Czech Mathematicians and Physicists.