Results 21 to 30 of about 124,717 (298)
Shortest Path Separators in Unit Disk Graphs [PDF]
To appear in ESA 2024.
Elfarouk Harb +2 more
openalex +5 more sources
Discrete Mathematics, 1990 Any given \(n\) points in the plane form the vertices of some graph by the convention that distinct points are adjacent whenever their distance is at most 2. The resulting graph is called a unit disk graph, since it is the intersection graph of the unit disks around the given \(n\) points.
Clark, Brent N. +2 more
openaire +1 more source
Improper Colourings of Unit Disk Graphs
Electronic Notes in Discrete Mathematics, 2005 AbstractMotivated by a satellite communications problem, we consider a generalized coloring problem on unit disk graphs. A coloring is k‐improper if no more than k neighbors of every vertex have the same colour as that assigned to the vertex. The k‐improper chromatic number χk(G) is the least number of colors needed in a k‐improper coloring of a graph ...
Havet, Frédéric +2 more
openaire +3 more sources
Balanced Line Separators of Unit Disk Graphs [PDF]
Computational Geometry, 2017 We prove a geometric version of the graph separator theorem for the unit disk intersection graph: for any set of $n$ unit disks in the plane there exists a line $\ell$ such that $\ell$ intersects at most $O(\sqrt{(m+n)\log{n}})$ disks and each of the halfplanes determined by $\ell$ contains at most $2n/3$ unit disks from the set, where $m$ is the ...
Carmi, Paz +8 more
openaire +3 more sources
Strongly Hyperbolic Unit Disk Graphs
, 2021 The class of Euclidean unit disk graphs is one of the most fundamental and well-studied graph classes with underlying geometry. In this paper, we identify this class as a special case in the broader class of hyperbolic unit disk graphs and introduce strongly hyperbolic unit disk graphs as a natural counterpart to the Euclidean variant.
Bläsius, Thomas +3 more
openaire +8 more sources
Families of Riemann Surfaces, Uniformization and Arithmeticity [PDF]
, 2016 A consequence of the results of Bers and Griffiths on the uniformization of complex algebraic varieties is that the universal cover of a family of Riemann surfaces, with base and fibers of finite hyperbolic type, is a contractible 2-dimensional domain ...
González-Diez, Gabino +1 more
core +2 more sources
On the Complexity of Target Set Selection in Simple Geometric Networks [PDF]
Discrete Mathematics & Theoretical Computer ScienceWe study the following model of disease spread in a social network. At first, all individuals are either infected or healthy. Next, in discrete rounds, the disease spreads in the network from infected to healthy individuals such that a healthy individual
Michal Dvořák +2 more
doaj +1 more source
Planar subgraphs without low-degree nodes [PDF]
, 2011 We study the following problem: given a geometric graph G and an integer k, determine if G has a planar spanning subgraph (with the original embedding and straight-line edges) such that all nodes have degree at least k.
A. Liebers +9 more
core +2 more sources
Complexity, 2020 In a wireless ad hoc network, the size of the virtual backbone (VB) is an important factor for measuring the quality of the VB. The smaller the VB is, the less the overhead caused by the VB.
Jiarong Liang +5 more
doaj +1 more source
Hierarchically specified unit disk graphs
Theoretical Computer Science, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marathe, Madhav V. +3 more
openaire +1 more source