A5005468020- Computational Geometry and Mesh Generation
- Advanced Graph Theory Research
- graph theory and CDMA systems
- Digital Image Processing Techniques
- Advanced Combinatorial Mathematics
- Limits and Structures in Graph Theory
- Graph Labeling and Dimension Problems
- Advanced Numerical Analysis Techniques
- Topological and Geometric Data Analysis
- semigroups and automata theory
- Data Management and Algorithms
- Optimization and Packing Problems
- Constraint Satisfaction and Optimization
- Optimization and Search Problems
- Point processes and geometric inequalities
- Mathematics and Applications
- Advanced Algebra and Logic
- Computability, Logic, AI Algorithms
- Advanced Topology and Set Theory
- Graph theory and applications
- Markov Chains and Monte Carlo Methods
- Complexity and Algorithms in Graphs
- Computer Graphics and Visualization Techniques
- Algorithms and Data Compression
- Stochastic processes and statistical mechanics
Technische Universität Berlin
2016-2025
Alfréd Rényi Institute of Mathematics
2021
Karlsruhe Institute of Technology
2021
Eötvös Loránd University
2021
University of Birmingham
2021
Berlin Mathematical School
2011-2020
University of Hagen
2020
Universitat de Barcelona
2020
Aix-Marseille Université
2020
Institute of Mathematics and Informatics
2020
The set of all orientations a planar graph with prescribed outdegrees carries the structure distributive lattice. This general theorem is proven in first part paper. In second applied to show that interesting combinatorial sets related have lattice structure: Eulerian orientations, spanning trees and Schnyder woods. For wood application some additional theory has be developed. particular it shown for induces dual.
This paper investigates the following question: Given an integer grid ϕ, where ϕ is a proper subset of plane or 3d space, which graphs admit straight-line crossingfree drawings with vertices located at points ϕ? We characterize trees that can be drawn on two dimensional c · n × к grid, and are given constants, consisting parallel horizontal lines infinite length. Motivated by results we investigate restrictions in 3 dimensions show every outerplanar graph crossing-free straight linear volume...
Planar bipartite graphs can be represented as touching of horizontal and vertical segments in $\mathbb{R}^2$. We study a generalization space, namely, axis-aligned rectangles $\mathbb{R}^3$. prove that planar $3$-colorable The result implies characterization corner polytopes previously obtained by Eppstein Mumford. A by-product our proof is distributive lattice structure on the set orthogonal surfaces with given skeleton. Moreover, we subclass strong representations, i.e., families...
We prove that every planar graph has a representation using axis-parallel cubes in three dimensions such way there is cube corresponding to each vertex of the and two have non-empty intersection if only their vertices are adjacent. Moreover, when intersection, they just touch other. This result strengthening by Thomassen which states boxes.
We consider several classes of intersection graphs line segments in the plane and prove new equality separation results between those classes. In particular, we show that: grounded downward rays form same graph class, not every is an rays, outer segment rays. The first result answers open problem posed by Cabello Jejčič. third confirms a conjecture Cabello. thereby completely elucidate remaining questions on containment relations these graphs. further characterize complexity recognition...
We deal with the asymptotic enumeration of combinatorial structures on planar maps. Prominent instances such problems are spanning trees, bipartite perfect matchings, and ice models. The notion orientations out-degrees prescribed by a function $\alpha:V\rightarrow {\Bbb N}$ unifies many different structures, including afore mentioned. call these $\alpha$-orientations. main focus this paper bounds for maximum number $\alpha$-orientations that map $n$ vertices can have, $\alpha$. give examples...