## Mathematicians from all around the world met in Domazlice

### Working in Domazlice on a solution of a long-standing
mathematical problem, the Matthews-Sumner Conjecture

#### Stanislav Sebek, Domazlicky denik, October 10, 2008

The fifth in a series of international mathematical workshops
attracted over 30 mathematicians from Europe, United States,
Australia and Japan, to Domazlice.

The meetings focus on the so-called Matthews-Sumner
Conjecture. "This is a graph theory problem that has been open for
25 years. Some questions [in graph theory] have easy answers, but
others lack a solution even after decades", explains Tomas Kaiser
from the University of West Bohemia.

"The main difference between this workshop and typical
mathematical conferences is that the workshop is primarily focused
on a single problem, which increases the chance of progress," says
Professor Zdenek Ryjacek from the University of West Bohemia in
Pilsen, which hosts the meeting, to our reporter.

According to Herbert Fleischner from Vienna, this is a good
approach. "The scope of most conferences is too broad, but here,
mathematicians from all around the world concentrate [on one
problem]. Moreover, I highly regard Czech mathematicians. For
instance, Professor Jaroslav Nesetril from Charles University, who
is also here, is among the best."

According to Fleischner, the best thing about the workshop is the
way all the experts in the field collaborate. "There is no rivalry
here. We do compete of course, but in a positive sense," he adds.

"We simply put our heads together and I think we are making
progress toward a solution. One of the participants recently solved
an important open problem by disproving [a related] conjecture that
some people worked on for years, but even that is a result and a
move forward," Kaiser says.

In Ryjacek's opinion, the best ideas come up in discussions
between colleagues in a friendly and informal setting. "Most of us
are in contact over email, but for a truly creative atmosphere,
meeting in person is essential," he claims. Hao Li from Paris
considers Domazlice and the Sokolsky dum hotel, the venue of the
workshop, to be an ideal place for the lectures and
discussions. "The atmosphere here is pleasant. I attended the
previous events as well, for instance in Hannover. I truly like the
historical town of Domazlice. The ambience and people here are
stimulating, I find new ideas," he adds.

[**Caption:** Looking for a solution. Mathematicians from all
around the world met in Domazlice to spend a week in expert talks
and discussions in a quiet atmosphere. Organizer Zdenek Ryjacek
(middle) claims that pleasant ambience is like a fertile soil for
ideas.]