A5083605241- Advanced Graph Theory Research
- Stochastic processes and statistical mechanics
- Limits and Structures in Graph Theory
- Advanced Combinatorial Mathematics
- Computational Geometry and Mesh Generation
- Graph theory and applications
- Graph Labeling and Dimension Problems
- Mathematical Dynamics and Fractals
- Markov Chains and Monte Carlo Methods
- Bayesian Methods and Mixture Models
- graph theory and CDMA systems
- Data Management and Algorithms
- Complexity and Algorithms in Graphs
- Optimization and Packing Problems
- Point processes and geometric inequalities
- Robotic Path Planning Algorithms
- Digital Image Processing Techniques
- Robotics and Sensor-Based Localization
- Cellular Automata and Applications
- Topological and Geometric Data Analysis
- Interconnection Networks and Systems
- semigroups and automata theory
- Advanced Mathematical Theories and Applications
- Random Matrices and Applications
- Mathematics and Applications
Universitat Politècnica de Catalunya
2014-2024
Centre de Recerca Matemàtica
2022-2024
Barcelona Graduate School of Mathematics
2014-2019
TU Wien
2013
We present a complete analytic solution to the problem of counting planar graphs. prove an estimate <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="g Subscript n Baseline tilde g dot Superscript negative 7 slash 2 gamma factorial"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>g</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>∼<!-- ∼ --></mml:mo> <mml:mo>⋅<!-- ⋅ <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−<!-- −...
Abstract Consider a family \documentclass{article}\usepackage{mathrsfs, amsmath, amssymb}\pagestyle{empty}\begin{document}\begin{align*}\mathcal{T}\end{align*}\end{document} of 3‐connected graphs moderate growth, and let amssymb}\pagestyle{empty}\begin{document}\begin{align*}\mathcal{G}\end{align*}\end{document} be the class whose components are in . We present general framework for analyzing such classes based on singularity analysis generating functions, which generalizes previously...
Let $G(n,M)$ be the uniform random graph with $n$ vertices and $M$ edges. Erdős Rényi (1960) conjectured that limiting probability \[ \lim _{n \to \infty } \mathrm {Pr}\{G(n,\textstyle {n\over 2}) \hbox { is planar}\} \] exists a constant strictly between $0$ $1$. Łuczak, Pittel Wierman (1994) proved this conjecture, Janson, Knuth (1993) gave lower upper bounds for probability. In paper we determine exact of being planar near critical point $M=n/2$. For each $\lambda$, find an analytic...
We prove that every triangle-free planar graph is the of intersection a set segments in plane.Moreover, can be chosen only three directions (horizontal, vertical and oblique) such way no two cross, i.e., intersect common interior point.
The Tutte polynomial is a notoriously hard graph invariant, and efficient algorithms for it are known only few special classes, like those of bounded tree‐width. notion clique‐width extends the definition cographs (graphs without induced $P_4$), more general than that We show subexponential algorithm (running in time $\exp{O(n^{1-\varepsilon})}\,$) computing on graphs clique‐width. In fact, our computes U‐polynomial.