Seminar of the Combinatorial Geometry Research Group

2023 Spring Semester - every Monday at 12:15 in room 3-110, ELTE

May 6, 2024
Lili Ködmön: Grid-drawings of graphs in three-dimensions

Bibliography:
József Balogh, Ethan Patrick White: Grid-drawings of graphs in three-dimensions, arXiv


April 29, 2024
Balázs Szabó: Coloring directed hypergraphs

Abstract: Lovász proved that any hypergraph containing no two hyperedges with intersection size one admits a proper 2-coloring. This result has several generalizations. One possible generalization of this result is that if we do not require for every pair of hyperedges to have an empty intersection or intersection with size at least two. Directed hypergraphs are hypergraphs in which the vertex set of each hyperedge is partitioned into two parts, a head and a tail. B. Keszegh and D. Pálvölgyi have the following conjecture. Let $H$ be a directed hypergraph such that in every hyperedge the number of head-vertices is less than the number of tail-vertices. Assume that for every pair of hyperedges $E_{1},E_{2}\in E(H)$, if $E_{1}\cap E_{2}=\{v\}$, then $v$ is a head-vertex in at least one of the hyperedges. Then $H$ admits a proper 2-coloring. B. Keszegh showed that the conjecture is true in the special case of 3-uniform hypergraphs. A directed 3-uniform hypergraph such that in every hyperedge the number of head-vertices is one and the number of tail-vertices is two is called $2\rightarrow 1$ hypergraph. In this talk I will prove that the conjecture is also true if every hyperedge has at most one head-vertex and I will talk about other sufficient conditions for $2\rightarrow 1$ hypergraphs to be proper $k$-colorable.


April 22, 2024
Balázs Keszegh: Extending simple monotone drawings

Bibliography:
Jan Kynčl, Jan Soukup: Extending simple monotone drawings, arXiv


April 15, 2024
Dániel Simon: Explicit unit distance graphs with exponential chromatic number and arbitrary girth

Bibliography:
Matija Bucić, James Davies: Explicit unit distance graphs with exponential chromatic number and arbitrary girth, arXiv


April 8, 2024
Arsenii Sagdeev: Turán Densities for Daisies and Hypercubes

Bibliography:
David Ellis, Maria-Romina Ivan, Imre Leader: Turán Densities for Daisies and Hypercubes, arXiv


April 1, 2024
No seminar (Easter)

March 25, 2024
Panna Gehér: Arithmetic progressions in Euclidean Ramsey theory

Bibliography:
Gabriel Currier, Kenneth Moore, Chi Hoi Yip: Any two-coloring of the plane contains monochromatic 3-term arithmetic progressions, arXiv
Jakob Führer, Géza Tóth: Progressions in Euclidean Ramsey theory, arXiv


March 18, 2024
Lili Ködmön: Note on $k$-Planar and Min-$k$-Planar Drawings of Graphs

Bibliography:
Petr Hliněný: Note on $k$-Planar and Min-$k$-Planar Drawings of Graphs, arXiv


March 11, 2024
Péter Ágoston: On prescribing total orders for bipartite sets of distances in euclidean plane

Bibliography:
Gerardo L. Maldonado, Miguel Raggi Pérez, Edgardo Roldán-Pensado: On prescribing total orders for bipartite sets of distances in euclidean plane, arXiv


March 4, 2024
Péter Ágoston: On prescribing total orders and preorders to pairwise distances of points in Euclidean space

Bibliography:
Víctor Hugo Almendra-Hernández, Leonardo Martínez-Sandoval: On prescribing total orders and preorders to pairwise distances of points in Euclidean space, Computational Geometry, Volume 107 (2022) (arXiv)


February 26, 2024
Attila Jung: On the Complexity of Recognizing Nerves of Convex Sets

Bibliography:
Patrick Schnider, Simon Weber: On the Complexity of Recognizing Nerves of Convex Sets, arXiv


February 19, 2024
Dömötör Pálvölgyi: Topological Drawings meet Classical Theorems from Convex Geometry

Bibliography:
Helena Bergold, Stefan Felsner, Manfred Scheucher, Felix Schröder, Raphael Steiner: Topological Drawings meet Classical Theorems from Convex Geometry, arXiv