On the Zarankiewicz problem for intersection hypergraphs

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...

Modern integrated circuits are tiny yet incredibly complex technological artifacts, composed of millions and billions of individual structures working in unison. Managing their complexity and facilitating their design drove part of the co-evolution of mode ...

Graph neural networks (GNNs) have demonstrated promising performance across various chemistry-related tasks. However, conventional graphs only model the pairwise connectivity in molecules, failing to adequately represent higher order connections, such as m ...

Surrogate-based optimization is widely used for aerodynamic shape optimization, and its effectiveness depends on representative sampling of the design space. However, traditional sampling methods are hard-pressed to effectively sample high-dimensional desi ...

Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem. Spectral algorithms ...

The recent geopolitical conflicts in Europe have underscored the vulnerability of the current energy system to the volatility of energy carrier prices. In the prospect of defining robust energy systems ensuring sustainable energy supply in the future, the ...

We examine the connection of two graph parameters, the size of a minimum feedback arcs set and the acyclic disconnection. A feedback arc set of a directed graph is a subset of arcs such that after deletion the graph becomes acyclic. The acyclic disconnecti ...

In this paper, we study sampling from a posterior derived from a neural network. We propose a new probabilistic model consisting of adding noise at every pre- and post-activation in the network, arguing that the resulting posterior can be sampled using an ...

The reported rate of the occurrence of unilateral spatial neglect (USN) is highly variable likely due to the lack of validity and low sensitivity of classical tools used to assess it. Virtual reality (VR) assessments try to overcome these limitations by pr ...

Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...

Graph machine learning offers a powerful framework with natural applications in scientific fields such as chemistry, biology and material sciences. By representing data as a graph, we encode the prior knowledge that the data is composed of a set of entiti ...

This work presents a graph neural network (GNN) framework for solving the maximum independent set (MIS) problem, inspired by dynamic programming (DP). Specifically, given a graph, we propose a DP-like recursive algorithm based on GNNs that firstly construc ...

Bioaerosols are emitted from various sources into the indoor environment and can positively and negatively impact human health. Humans are the major source of bioaerosol emissions indoors, specifically for bacteria. However, efficient sampling to guarantee ...

An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n. Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed ...

Maximal subgraph mining is increasingly important in various domains, including bioinformatics, genomics, and chemistry, as it helps identify common characteristics among a set of graphs and enables their classification into different categories. Existing ...

We prove that for any triangle-free intersection graph of n axis-parallel line segments in the plane, the independence number alpha of this graph is at least alpha n/4+ohm(root n). We complement this with a construction of a graph in this class satisfying ...

Various forms of real-world data, such as social, financial, and biological networks, can be represented using graphs. An efficient method of analysing this type of data is to extract subgraph patterns, such as cliques, cycles, and motifs, from graphs. For ...

The recent geopolitical conflicts in Europe highlighted the sensibility of the current energy system to the volatility of energy carrier prices. In the prospect of defining robust energy system configurations to ensure energy supply stability, it is necess ...

This paper presents a novel distributed approach for solving AC power flow (PF) problems. The optimization problem is reformulated into a distributed form using a communication structure corresponding to a hypergraph, by which complex relationships between ...

When can a unimodular random planar graph be drawn in the Euclidean or the hyperbolic plane in a way that the distribution of the random drawing is isometry-invariant? This question was answered for one-ended unimodular graphs in Benjamini and Timar, using ...

On the Zarankiewicz problem for intersection hypergraphs

Chat with Graph Search

Non-planarity of Markoff graphs mod p

Graph generative deep learning models with an application to circuit topologies

Molecular hypergraph neural networks

DiffAirfoil: An Efficient Novel Airfoil Sampler Based on Latent Space Diffusion Model for Aerodynamic Shape Optimization

The Power of Two Matrices in Spectral Algorithms for Community Recovery

Identification of typical district configurations: A two-step global sensitivity analysis framework

The connection of the acyclic disconnection and feedback arc sets - On an open problem of Figueroa et al

Gibbs sampling the posterior of neural networks

An immersive virtual reality tool for assessing left and right unilateral spatial neglect

A Note on Lenses in Arrangements of Pairwise Intersecting Circles in the Plane

Equivariant Neural Architectures for Representing and Generating Graphs

Maximum Independent Set: Self-Training through Dynamic Programming

Comparison of two methods for bioaerosol sampling and characterization in a low-biomass chamber environment

Results on Sparse Integer Programming and Geometric Independent Sets

Scalable maximal subgraph mining with backbone-preserving graph convolutions

ON THE INDEPENDENCE NUMBER OF INTERSECTION GRAPHS OF AXIS-PARALLEL SEGMENTS

Acceleration of graph pattern mining and applications to financial crime

Identification of typical district configurations: A two-step global sensitivity analysis framework

Hypergraph-Based Fast Distributed AC Power Flow Optimization

A full characterization of invariant embeddability of unimodular planar graphs