Concept

Nombre de croisements (théorie des graphes)

Publications associées (26)

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Approximating the rectilinear crossing number

János Pach

A straight-line drawing of a graph G is a mapping which assigns to each vertex a point in the plane and to each edge a straight-line segment connecting the corresponding two points. The rectilinear crossing number of a graph G, (cr) over bar (G), is the mi ...

2019

Vector-Based 3D Graphic Statics: a framework for the design of spatial structures based on the relation between form and forces

Corentin Jean Dominique Fivet, Pierluigi D'Acunto

This article develops a vector-based 3D graphic statics framework that uses synthetic and intuitive graphical means for the analysis and design of spatial structures such as networks of bar elements in static equilibrium. It is intended to support the coll ...

2019

New Notions and Constructions of Sparsification for Graphs and Hypergraphs

Ola Nils Anders Svensson

A sparsifier of a graph G (Bencztir and Karger; Spielman and Teng) is a sparse weighted subgraph (G) over tilde that approximately retains the same cut structure of G. For general graphs, non-trivial sparsification is possible only by using weighted graphs ...

IEEE COMPUTER SOC2019

Thrackles: An improved upper bound

János Pach, Radoslav Fulek

A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, ex ...

ELSEVIER SCIENCE BV2019

Asyrnptotics for the Turan number of Berge-K-2,K-t

Abhishek Methuku

Let F be a graph. A hypergraph is called Berge-F if it can be obtained by replacing each edge in F by a hyperedge containing it. Let F be a family of graphs. The Turan number of the family Berge-F is the maximum possible number of edges in an r-uniform hyp ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2019

On approximation algorithms and polyhedral relaxations for knapsack problems, and clustered planarity testing

Igor Malinovic

Knapsack problems give a simple framework for decision making. A classical example is the min-knapsack problem (MinKnap): choose a subset of items with minimum total cost, whose total profit is above a given threshold. While this model successfully general ...

EPFL2019

On the Turan number of ordered forests

Gábor Tardos, Istvan Tomon, Dániel József Korándi

An ordered graph H is a simple graph with a linear order on its vertex set. The corresponding Turan problem, first studied by Pach and Tardos, asks for the maximum number ex(

ACADEMIC PRESS INC ELSEVIER SCIENCE2019

Note on k-planar crossing numbers

János Pach

The crossing number CR(G) of a graph G = (V, E) is the smallest number of edge crossings over all drawings of G in the plane. For any k >= 1, the k-planar crossing number of G, CRk(G), is defined as the minimum of CR(G(0)) + CR(G(1)) + ... + CR(G(k-i)) ove ...

Elsevier Science Bv2018

Graph-based structures in data science

Nathanaël Perraudin

State-of-the-art data analysis tools have to deal with high-dimensional data. Fortunately, the inherent dimensionality of data is often much smaller, as it has an internal structure limiting its degrees of freedom. In most cases, this structure can be appr ...

EPFL2017

Song Recommendation with Non-Negative Matrix Factorization and Graph Total Variation

Pierre Vandergheynst, Kirell Maël Benzi, Xavier Bresson, Vasilis Kalofolias

This work formulates a novel song recommender system as a matrix completion problem that benefits from collaborative filtering through Non-negative Matrix Factorization (NMF) and content-based filtering via total variation (TV) on graphs. The graphs encode ...

Ieee2016