Concept

Neighbourhood (graph theory)

Related publications (87)

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Community detection enhancement in networks using proper weighting and partial synchronization

Martin Hasler, Ali Ajdari Rad, Alireza Khadivi

A community in a network is a subset of vertices densely connected to each other, but less connected to the vertices outside. Many different approaches have been developed to find such structures in a given network, but the main drawback of most of the ava ...

IEEE2010

Community Detection Enhancement in Networks using Proper Weighting and Partial Synchronization

Martin Hasler, Ali Ajdari Rad, Alireza Khadivi

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

A Computational Approach to Conway's Thrackle Conjecture

János Pach, Radoslav Fulek

A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely once, either at a common vertex or at a proper crossing. Let t(n) denote the maximum number of edges that a thrackle of n vertices can have. According to a 40 yea ...

Springer2010

A Magnetic Procedure for the Stability Number

Dominique de Werra

A magnet is a pair u, v of adjacent vertices such that the proper neighbours of u are completely linked to the proper neighbours of v. It has been shown that one can reduce the graph by removing the two vertices u, v of a magnet and introducing a new verte ...

2009

Mixed graph edge coloring

Bernard Ries

We are interested in coloring the edges of a mixed graph. i.e., a graph containing unoriented and oriented edges. This problem is related to a communication problem in job-shop scheduling systems. In this paper we give general bounds oil the number of requ ...

Elsevier2009

2D-TUCKER Is PPAD-Complete

Tucker's lemma states that if we triangulate the unit disc centered at the origin and color the vertices with {1, 1,2, 2} in an antipodal way (if vertical bar z vertical bar = 1, then the sum of the colors of z and -z is zero), then there must be an edge F ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2009

Degenerate crossing numbers

János Pach

Let G be a graph with n vertices and ea parts per thousand yen4n edges, drawn in the plane in such a way that if two or more edges (arcs) share an interior point p, then they properly cross one another at p. It is shown that the number of crossing points, ...

Springer-Verlag2009

Graph coloring with cardinality constraints on the neighborhoods

Dominique de Werra, Bernard Ries

Extensions and variations of the basic problem of graph coloring are introduced. The problem consists essentially in finding in a graph G a k-coloring, i.e., a partition V-1,...,V-k of the vertex set of G such that, for some specified neighborhood (N) over ...

2009

Networks of Mixed Canonic-Dissipative Systems and Dynamic Hebbian Learning

Max-Olivier Hongler, Julio Rodriguez

We consider a collection {O_k}_{k=1}^N of interacting parametric mixed canonical-dissipative systems, (MCD). Each individual Ok, exhibits, in absence of interaction, a limit cycle L_k on which the orbit circulation is parameterized by w_k(t). The underlyin ...

Shaker Verlag2008

On two coloring problems in mixed graphs

Dominique de Werra, Bernard Ries

We are interested in coloring the vertices of a mixed graph, i.e., a graph containing edges and arcs. We consider two different coloring problems: in the first one we want adjacent vertices to have different colors and the tail of an arc to get a color str ...

2008