Thesis supervisor: János Pach
Location of studies (in Hungarian): ELKH Rényi Institute Abbreviation of location of studies: BME
Description of the research topic:
A geometric graph is a graph drawn in the plane such that its vertices are points in general position and its edges are straight-line segments between these points. Topological graphs are defined in the same way, except that now curvilinear edges are permitted. There are many interesting results and open problems on geometric and topological graphs that are relevant to well known questions in discrete and computational geometry, graph drawing, and additive combinatorics, such as the halving line problem (Erdős–Lovász–Simmons–Straus), questions on repeated distances and incidences (Erdős, Szemerédi–Trotter), etc. To settle these problems, we need to further develop the structural and extremal theory of intersection patterns of geometric objects.
Required language skills: English Further requirements: Knowledge of graph theory, advanced combinatorics, probabilistic and algebraic methods.
Number of students who can be accepted: 1
Deadline for application: 2024-05-31
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
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