A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Note on Geometric Graphs

2000
*
Journal of combinatorial theory. Series A
*

We show that a

doi:10.1006/jcta.1999.3001
fatcat:jidzw242hnejtjciz5dr7wgs5y
*geometric**graph*of n vertices with no k + 1 pairwise disjoint edges has at most 2 9 k 2 n edges. ... A*geometric**graph*is a*graph*drawn in the plane so that the vertices are represented by points in general position, the edges are represented by straight line segments connecting the corresponding points ... In this*note*we further improve the upper bound. Theorem 1. For any k < n/2, e k (n) ≤ 2 9 k 2 n. Let G be a*geometric**graph*. ...##
###
A note on light geometric graphs

2013
*
Discrete Mathematics
*

Let G be a

doi:10.1016/j.disc.2013.03.001
fatcat:w6dv2d5f7ra4dnyskpuxaysckq
*geometric**graph**on*n vertices in general position in the plane. ... We extend the previous result in [1] and with a shorter argument show that every k-light*geometric**graph**on*n vertices has at most O(n √ k) edges. This bound is best possible. ... Lemma 2. 1 . 1 Let G be an oriented*geometric**graph**on*n vertices. ...##
###
A note on harmonic subgraphs in labelled geometric graphs

2008
*
Information Processing Letters
*

In this

doi:10.1016/j.ipl.2007.08.016
fatcat:tvlfpmn2pnhudf3zypa7r4h5m4
*note*we investigate the maximum size of noncrossing matchings and paths*on*S, under the requirement that no two edges have the same weight. ... Introduction The study of*geometric**graphs**on*point sets in the plane has received a considerable amount of attention lately [6, 8] . ...*Note*that in these questions, the labelling map is two-to-*one*. ...##
###
On Spanners of Geometric Graphs
[chapter]

2006
*
Lecture Notes in Computer Science
*

Previously, this NP-hardness result was only known for non-

doi:10.1007/11785293_36
fatcat:dq7uksrjgjbrfjye7vjd6yj6me
*geometric**graphs*. ... Given a connected*geometric**graph*G, we consider the problem of constructing a tspanner of G having the minimum number of edges. ... Workshop*on*Algorithm Theory, Lecture*Notes*in Computer Science, Volume 4059, Springer-Verlag, 2006, 388-399. ...##
###
Parameterized Complexity of Independence and Domination on Geometric Graphs
[chapter]

2006
*
Lecture Notes in Computer Science
*

We investigate the parameterized complexity of Maximum Independent Set and Dominating Set restricted to certain

doi:10.1007/11847250_14
fatcat:bd5ydgcicvc25cqq2ju3vdc35i
*geometric**graphs*. ... We show that Dominating Set is W[1]-hard for the intersection*graphs*of unit squares, unit disks, and line segments. ... Therefore, it is an interesting question to investigate the complexity of these problems*on*different types of*geometric**graphs*. ...##
###
On the Cover Time of Random Geometric Graphs
[chapter]

2005
*
Lecture Notes in Computer Science
*

A random

doi:10.1007/11523468_55
fatcat:poeylyoy7fdzpojq33yyyf4h4i
*geometric**graph*G(n, r) is obtained by placing n points uniformly at random*on*the unit square and connecting two points iff their Euclidean distance is at most r. ... Recently, with the advent of ad-hoc and sensor networks, an interesting class of random*graphs*, namely random*geometric**graphs*, has gained new relevance and its properties have been the subject of much ...*Note*immediately last corollary that this yields negative results for G 1 (n, r) in that optimality of cover time for*one*-dimensional*geometric**graphs*requires a radius of order strictly greater than the ...##
###
On Paths in a Complete Bipartite Geometric Graph
[chapter]

2001
*
Lecture Notes in Computer Science
*

A

doi:10.1007/3-540-47738-1_17
fatcat:3btm6riw4rd55atqv55erxzdde
*geometric*complete bipartite*graph*K(A, B) is a complete bipartite*graph*with partite sets A and B which is drawn in the plane such that each edge of K (A, B) is a straight-line segment. ... We prove that (i) If |B| ≥ (n + 1)(2n − 4) + 1, then the*geometric*complete bipartite*graph*K(A, B) contains a path that passes through all the points in A and has no crossings; and (ii) There exists a ... If a*geometric**graph*G is a complete bipartite*graph*with partite sets A and B, i.e., V (G) = A ∪ B, then G is denoted by K(A, B), which may be called a*geometric*complete bipartite*graph*. ...##
###
Large Scale Simulations of a Neural Network Model for the Graph Bisection Problem on Geometrically Connected Graphs

2004
*
Electronic Notes in Discrete Mathematics
*

In this work some preliminary numerical results obtained by large scale simulations of the sequential dynamics of a neural network model for the

doi:10.1016/j.endm.2004.06.024
fatcat:7njsxz3v3vaxhbrzlhuiwqy6q4
*graph*bisection problem*on*random*geometrically*connected ...*graphs*are presented. ...*geometrically*connected*graphs*. ...##
###
Small Worlds and Rapid Mixing with a Little More Randomness on Random Geometric Graphs
[chapter]

2011
*
Lecture Notes in Computer Science
*

Let the G1 new wiring be such that we form a random cubic

doi:10.1007/978-3-642-20757-0_22
fatcat:n6ahax7lnjdr7n64njs3bsuczi
*graph*amongst the bin-leaders and superimpose this upon the random*geometric**graph*. ... Let the G2 new wiring be such that we form a random 1-out*graph*amongst the bin-leaders and superimpose this upon the random*geometric**graph*. ... Either random or deterministic. 2*Note*that if a*geometric**graph*is μ1-geo-dense then it is also μ2-geo-dense for any μ2 < μ1. ...##
###
On Geometric Structure of Global Roundings for Graphs and Range Spaces
[chapter]

2004
*
Lecture Notes in Computer Science
*

path hypergraph of a series-parallel

doi:10.1007/978-3-540-27810-8_39
fatcat:4dwa2ochwvdn3nrjshrjkmxhca
*graph*. ... We study*geometric*(or combinatorial) structure of the set of global roundings of a using the notion of compatible set with respect to the discrepancy distance. ... Also, they thank Ken-ichi Kawarabayashi and Takao Nishizeki for providing knowledge*on*the structure of series-parallel*graphs*. ...##
###
A note on a theorem of Perles concerning non-crossing paths in convex geometric graphs

2009
*
Computational geometry
*

Acknowledgements I would like to thank Eduardo Rivera-Campo, Gyula Károlyi and an anonymous referee for their suggestions about the presentation of this

doi:10.1016/j.comgeo.2008.07.002
fatcat:k6cqqhvwdbgzdnzurtjwoqnf3u
*note*. ...*Note*that |Z | = 2|P |. ... If P is in convex position then G is called a convex*geometric**graph*. A non-crossing path in a*geometric**graph*is a path which does not contain any intersecting pair of edges. ...##
###
On Local Transformations in Plane Geometric Graphs Embedded on Small Grids
[chapter]

2004
*
Lecture Notes in Computer Science
*

Given two n-vertex plane

doi:10.1007/978-3-540-24767-8_3
fatcat:ohv2oerp6bhxvledkhm74os3bu
*graphs*G 1 = (V 1 , E 1 ) and G 2 = (V 2 , E 2 ) with |E 1 | = |E 2 | embedded in the n × n grid, with straightline segments as edges, we show that with a sequence of O(n) point ...*Note*that there is a discrepancy between the combinatorial result and the*geometric**one*. ...*Note*that point moves do not change the connectivity of a*graph*. Therefore, we solely need to concentrate*on*edge moves. The main tool we used for edge moves in triangulations is Lemma 1. ...##
###
Bounds on the Geometric Mean of Arc Lengths for Bounded-Degree Planar Graphs
[chapter]

2009
*
Lecture Notes in Computer Science
*

Cache-oblivious layouts, constructed to minimize the

doi:10.1007/978-3-642-02270-8_17
fatcat:fuak46wvkveoxjia6n4c5mdto4
*geometric*mean of arc lengths of*graphs*, have been adapted to reduce data access time during random walks*on**graphs*. ... In this paper, we present a constant factor approximation algorithm for the Minimum*Geometric*Mean Layout (MGML) problem for bounded-degree planar*graphs*. ... This observation strongly supported that there is possibility that we can have a constant-factor approximation algorithm in terms of minimizing the*geometric*means. ...##
###
The Domination Number of On-line Social Networks and Random Geometric Graphs
[chapter]

2015
*
Lecture Notes in Computer Science
*

Asymptotic sublinear bounds are rigorously derived for the domination number of

doi:10.1007/978-3-319-17142-5_14
fatcat:45edczldybfnpo42jd4awydz44
*graphs*generated by the memoryless*geometric*protean random*graph*model. ... In addition, we derive the asymptotic value of the domination number in classical random*geometric**graphs*. ... The basic reference*on*random*geometric**graphs*is the monograph by Penrose [32] . ...##
###
On Radio Broadcasting in Random Geometric Graphs
[chapter]

*
Lecture Notes in Computer Science
*

Since this

doi:10.1007/978-3-540-87779-0_15
fatcat:ja54jfje25abnmw57hr3gsad7q
*graph*is usually not strongly connected, we assume that the message which has to be spread to all nodes of the*graph*is placed initially in*one*of the nodes of the giant component. ... In this paper we consider radio broadcasting in random*geometric**graphs*, in which n nodes are placed uniformly at random in [0, √ n] 2 , and there is a (directed) edge from a node u to a node v in the ... The results of Theorems 3 and 4 can be extended to further random*geometric**graph*models. ...
« Previous

*Showing results 1 — 15 out of 357,754 results*