PavelFest

In honour of the scientific achievements of Pavel Valtr and to celebrate his 60th birthday, we organize an event PavelFest on Sunday, May 24, in the downtown of Prague, on the second floor of the building of Charles University, Malostranské náměstí­ 25 (room S5, 2nd floor).

The event is organized by Martin Balko, Viola Mészáros, and Maria Saumell.

We would also like to thank everyone who helped with the organization and preparation of the event, in particular Petra Příhodová, Honza Kratochvíl, Jelena Glišić, Günter Rote, Adele Zita Rothe, Daniel Perz, Helena Nyklová, Jakub Černý, and Josef Cibulka.

Tentative schedule

Sunday May 24, 2026
Opening	13:50 – 14:00
First session	14:00 – ca. 15:15
	Jan Kratochvíl: How many paths lead to a good beer
	Imre Bárány: My joint works with Pavel Valtr
	Stefan Felsner: 1-Planar Drawings of Products of Cycles
Coffee Break	15:15 – 15:45
Second session	15:45 – ca. 17:30
	János Pach: Pavelovian reflections
	Birgit Vogtenhuber: Flipping Non-Crossing Spanning Trees
	Géza Tóth: Matchstick graphs and generalizations
	Jan Kratochvíl: Toulky s Pavlem

Abstracts

Jan Kratochvíl: How many paths lead to a good beer

How many edge-disjoint non-self-crossing Hamiltonian paths are guaranteed to exist in any complete geometric graph determined by n points in general position? The gap between the best known lower and upper bounds is horrendous - 3 paths always exist, while there are point sets which do not allow for more than n/3 paths. In hope to be able to improve the lower bound, the research has recently concentrated on proving the existence of 2 or 3 paths with further constraints, such as prescribing the end-points, forbidding some edges etc. We will survey the most recent results in this direction.

Imre Bárány: My joint works with Pavel Valtr

I will explain some of our joint results and their applications, consequences, and extensions.

Stefan Felsner: 1-Planar Drawings of Products of Cycles

We show the Cartesian product of two cycles C_m x C_n, i.e. the m x n toroidal grid, admits exactly three distinct simple 1-planar drawings when 5 <= m <= n. These drawings have (m-2)n, m(n-2), and mn - 4 crossings, respectively. As a corollary, we obtain that the 1-planar crossing number of C_m \times C_n with 3 <= m <= n is (m-2)n. This confirms, in the 1-planar setting, a conjecture of Harary, Kainen, and Schwenk. The drawings have the property that the n fundamental cycles C_m and the m fundamental cycles C_n of C_m x C_n form two classes of pairwise disjoint cycles. In fact establishing this property is a crucial step in our proof. (joint work with Kolja Knauer, Yasumi Kogo, and Bobby Miraftab)

János Pach: Pavelovian reflections

There are two kinds of mathematicians: problem solvers and theory builders. Pavel Valtr belongs to the first group, specializing in Erdős-type problems in discrete geometry. I will reflect on his contributions to some major unsolved problems in the field, including (1) the problem of repeated distances, (2) the number of edges in quasi-planar graphs, and (3) crossing families.

Birgit Vogtenhuber: Flipping Non-Crossing Spanning Trees

I will talk about flips in non-crossing geometric spanning trees on convex point sets. A flip sequence between two non-crossing spanning trees is a sequence single edge exchanges such that each intermediate structure is again a non-crossing spanning tree on the point set. Any two such non-crossing spanning trees can be transformed into each other with a finite number of flips. I will review old and recent results concerning bounds on the number of flips that are sometimes required and always sufficient. This talk is based on joint work with Havard Bakke Bjerkevik, Joseph Dorfer, Linda Kleist, and Torsten Ueckerdt.

Géza Tóth: Matchstick graphs and generalizations

A matchstick graph is a plane graph, drawn with unit segments as edges. In 2024 Lavollée and Swanepoel determined the maximum number of edges of matchstick graphs. We review several generalizations of their theorem and some related results.

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