Concept

Bipartite hypergraph

Publications associées (18)

Molecular hypergraph neural networks

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 ...

Aip Publishing2024

Hypergraph-Based Fast Distributed AC Power Flow Optimization

Colin Neil Jones, Yuning Jiang, Yingzhao Lian, Xinliang Dai

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 ...

IEEE2023

Motif Cut Sparsifiers

Mikhail Kapralov, Mikhail Makarov, Jakab Tardos

A motif is a frequently occurring subgraph of a given directed or undirected graph G (Milo et al.). Motifs capture higher order organizational structure of G beyond edge relationships, and, therefore, have found wide applications such as in graph clusterin ...

IEEE COMPUTER SOC2022

Towards Tight Bounds for Spectral Sparsification of Hypergraphs

Mikhail Kapralov, Jakab Tardos

Cut and spectral sparsification of graphs have numerous applications, including e.g. speeding up algorithms for cuts and Laplacian solvers. These powerful notions have recently been extended to hypergraphs, which are much richer and may offer new applicati ...

ASSOC COMPUTING MACHINERY2021

On subgraphs of C-2k-free graphs and a problem of Kuhn and Osthus

Abhishek Methuku

Let c denote the largest constant such that every C-6-free graph G contains a bipartite and C-4-free subgraph having a fraction c of edges of G. Gyori, Kensell and Tompkins showed that 3/8

2020

Linearity of saturation for Berge hypergraphs

Abhishek Methuku

For a graph F, we say a hypergraph H is a Berge-F if it can be obtained from F by replacing each edge of F with a hyperedge containing it. We say a hypergraph is Berge-F-saturated if it does not contain a Berge-F, but adding any hyperedge creates a copy of ...

ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD2019

Saturation of Berge hypergraphs

Abhishek Methuku

Given a graph F, a hypergraph is a Berge-F if it can be obtained by expanding each edge in F to a hyperedge containing it. A hypergraph H is Berge-F-saturated if H does not contain a subhypergraph that is a Berge-F, but for any edge e is an element of E((H ...

Elsevier2019

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. ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2019

Finding Perfect Matchings in Bipartite Hypergraphs

Chidambaram Annamalai

Haxell's condition [14] is a natural hypergraph analog of Hall's condition, which is a well-known necessary and sufficient condition for a bipartite graph to admit a perfect matching. That is, when Haxell's condition holds it forces the existence of a perf ...

SPRINGER HEIDELBERG2018

Monochromatic cycle covers in random graphs

Dániel József Korándi

A classic result of Erdos, Gyarfas and Pyber states that for every coloring of the edges of K-n with r colors, there is a cover of its vertex set by at most f(r)=O(r2logr) vertex-disjoint monochromatic cycles. In particular, the minimum number of such cove ...

WILEY2018

Combinatorial Algorithm for Restricted Max-Min Fair Allocation

Ola Nils Anders Svensson, Christos Kalaitzis, Chidambaram Annamalai

We study the basic allocation problem of assigning resources to players to maximize fairness. This is one of the few natural problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, a certain ...

Association for Computing Machinery2017

A Polynomial Regularity Lemma For Semialgebraic Hypergraphs And Its Applications In Geometry And Property Testing

János Pach

In this paper, we prove several extremal results for geometrically defined hypergraphs. In particular, we establish an improved lower bound, single exponentially decreasing in k, on the best constant delta > 0 such that the vertex classes P-1,...,P-k of ev ...

Society for Industrial and Applied Mathematics2016

On the Zarankiewicz problem for intersection hypergraphs

János Pach

Let d and t be fixed positive integers, and let denote the complete d-partite hypergraph with t vertices in each of its parts, whose hyperedges are the d-tuples of the vertex set with precisely one element from each part. According to a fundamental theorem ...

Academic Press Inc Elsevier Science2016

Combinatorial Algorithm for Restricted Max-Min Fair Allocation

Ola Nils Anders Svensson, Christos Kalaitzis, Chidambaram Annamalai

We study the basic allocation problem of assigning resources to players so as to maximize fairness. This is one of the few natural problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, a ce ...

2015

Overlap properties of geometric expanders

The overlap number of a finite (d + 1)-uniform hypergraph H is the largest constant c(H) is an element of (0, 1] such that no matter how we map the vertices of H into R-d, there is a point covered by at least a c(H)-fraction of the simplices induced by the ...

De Gruyter2011

Minimum d-blockers and d-transversals in graphs

Dominique de Werra

We consider a set V of elements and an optimization problem on V: the search for a maximum (or minimum) cardinality subset of V verifying a given property a"similar to. A d-transversal is a subset of V which intersects any optimum solution in at least d el ...

2011

Preemptive open shop scheduling with multiprocessors: polynomial cases and applications

Dominique de Werra

This paper addresses a multiprocessor generalization of the preemptive open-shop scheduling problem. The set of processors is partitioned into two groups and the operations of the jobs may require either single processors in either group or simultaneously ...

2008

Variations of coloring problems related to scheduling and discrete tomography

Bernard Ries

The graph coloring problem is one of the most famous problems in graph theory and has a large range of applications. It consists in coloring the vertices of an undirected graph with a given number of colors such that two adjacent vertices get different col ...

EPFL2007