A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
The edge-isoperimetric problem for discrete tori

2002
*
Discrete Mathematics
*

*The*

*edge*-

*isoperimetric*

*problem*has long been solved

*for*cartesian powers of

*the*cycles C3 and C4,

*for*which

*the*lexicographic order is

*the*optimal order, and powers of

*the*cycles Cn with n ¿ 5, which do ...

*For*powers of C5, it is clear that

*the*lexicographic order is not optimal. We present a solution to

*the*

*edge*-

*isoperimetric*

*problem*

*for*powers of C5 in

*the*form of an optimal order

*for*

*the*vertices. ...

*The*author would like to thank Sergei Bezrukov and Larry Harper

*for*posing

*the*

*problem*and providing comments on

*the*work presented here, and Dr. ...

##
###
The vertex isoperimetric problem for the powers of the diamond graph

2008
*
Discrete Mathematics
*

We introduce a new graph

doi:10.1016/j.disc.2007.04.060
fatcat:yhoairxe6bd3vge4jqjs5bqg3e
*for*all whose cartesian powers*the*vertex*isoperimetric**problem*has nested solutions. ... We present an exact solution to*the*vertex*isoperimetric**problem*on our graph by introducing a new class of orders that unifies all known*isoperimetric*orders defined on*the*cartesian powers of graphs. ...*The*compression technique we use here is a classical tool*for*dealing with*discrete**isoperimetric**problems*, see e.g., [8] . ...##
###
Page 4033 of Mathematical Reviews Vol. , Issue 2003f
[page]

2003
*
Mathematical Reviews
*

4033 05C Graph theory
2003£:05069 05C35 90C35
Carlson, Thomas A. (1-WA; Seattle, WA)

*The**edge*-*isoperimetric**problem**for**discrete**tori*. (English summary)*Discrete*Math. 254 (2002), no. 1-3, 33—49. ...*The*author considers an*edge*-*isoperimetric**problem**for**the*Carte- sian products of cycles. ...##
###
On k-ary n-cubes: theory and applications

2003
*
Discrete Applied Mathematics
*

In particular,

doi:10.1016/s0166-218x(02)00238-x
fatcat:aeqcxwdkmfh6na2lh2ir7t4q4q
*the**problem*of characterizing*the*subgraph of a given number of nodes with*the*maximum*edge*count is studied. ... 7 Many parallel processing applications have communication patterns that can be viewed as graphs called k-ary n-cubes, whose special cases include rings, hypercubes and*tori*. ... Acknowledgements 27*The*authors wish to thank*the*referees*for*their helpful comments and constructive suggestions. 29 ...##
###
Page 5517 of Mathematical Reviews Vol. , Issue 2000h
[page]

2000
*
Mathematical Reviews
*

Chapter 4 (Invariant

*tori*) concerns*the**problem*of*the*existence of invariant*tori*and*the*persistence of stable*tori*under small perturbations of*the*initial system. ... Namely, if*the**isoperimetric*quotient of*the*initial interface does not differ much from*the**isoperimetric*quotient of*the*Wulff shape, then*the*interface shrinks to a point in finite time and*the*isoperi ...##
###
Embedding hypercubes into cylinders, snakes and caterpillars for minimizing wirelength

2011
*
Discrete Applied Mathematics
*

Further, we show that

doi:10.1016/j.dam.2011.07.003
fatcat:xgh2riwonng25pglaheegkomwm
*the**edge**isoperimetric**problem*solves*the*wirelength*problem*of regular graphs and, in particular, hypercubes into triangular snakes and caterpillars. ... We consider*the**problem*of embedding hypercubes into cylinders to minimize*the*wirelength. ... Further, this solves*the*wirelength*problem*of powers of*the*Petersen graph [5] and*discrete**tori*[9] into triangular snakes and caterpillars. ...##
###
Sobolev spaces on graphs

2005
*
Quaestiones Mathematicae. Journal of the South African Mathematical Society
*

It is not difficult to show that

doi:10.2989/16073600509486144
fatcat:5eetkcnoljgazpzicgnturqo2y
*for**discrete**tori**the*estimate from (1) is optimal, up to a multiplicative constant. ... 11]). (2) Inequalities between*discrete*Sobolev seminorms (corresponding to two different*edge*sets and*the*same value of p) are very important*for**the**problem*of l p -embeddability of graph metrics, see ...##
###
Isoperimetric and Sobolev inequalities for magnetic graphs
[article]

2020
*
arXiv
*
pre-print

Using heat kernel techniques, we also give lower bounds

arXiv:2005.10409v1
fatcat:alg2oap2m5g53mdwlqxj2zhahy
*for**the*eigenvalues of*the**discrete*magnetic Laplacian. ... We introduce a concept of*isoperimetric*dimension*for*magnetic graphs, that is, graphs where every*edge*is assigned a complex number of modulus one. ... Acknowledgements*The*author thanks Profs. William B. Johnson and Keri Kornelson*for*helpful discussions on*the*subject of this paper. ...##
###
Stable periodic constant mean curvature surfaces and mesoscopic phase separation

2007
*
Interfaces and free boundaries (Print)
*

We give a first comprehensive description of

doi:10.4171/ifb/168
fatcat:ubs63obb5nfjde5shk5zop5xb4
*the*stable solutions of*the*periodic*isoperimetric**problem*in*the*case of lattice symmetry. ... We prove that closed, stable, constant mean curvature surfaces in R 3 /Γ , Γ ⊂ R 3 being a*discrete*subgroup of translations with rank k, have genus k. ... According to Surface Evolver experiments [22] ,*the**isoperimetric**problem*in other 3-*tori*, like*the*face centered cubic torus, should admit solutions of genus 2. ...##
###
A local–global principle for vertex-isoperimetric problems

2002
*
Discrete Mathematics
*

We consider

doi:10.1016/s0012-365x(02)00431-4
fatcat:ezit4iaclbavrnxysadhx2o6ii
*the*vertex-*isoperimetric**problem*(VIP)*for*cartesian powers of a graph G. ... In this paper we consider*the*vertex-*isoperimetric**problem*(VIP) on graphs. Let G = (V; E) be a ÿnite simple graph, and let A ⊆ V . ... Acknowledgements*The*authors are grateful to two anonymous referees*for*their constructive comments that signiÿcantly improved*the*quality of*the*paper. ...##
###
Isoperimetric inequalities and Dirichlet functions of Riemann surfaces

1994
*
Publicacions matemàtiques
*

integral in

doi:10.5565/publmat_38194_19
fatcat:kmferx56ijf6fiaacvpshpcpki
*the*surface . ... We prove too, by an example, that*the*implication is not tru e without*the*condition of regularity. ... ~D arc cosh coth 2*The*vertices of G ar e*the*vertices of T .*The**edges*of G are*the*union of*the**edges*of T an d*the**edges*of G,,, ,*for*all n~1 .*The*root ro of G has degree two . ...##
###
3D GEOMETRIC CHARACTERIZATION OF PARTICLES APPLIED TO TECHNICAL CLEANLINESS

2012
*
Image Analysis and Stereology
*

However,

doi:10.5566/ias.v31.p163-174
fatcat:x7uslhjkvfa2xn6ddjjteowr5u
*the*particle's shape is decisive*for**the*damage it can cause, yet can not be judged reliably from 2d data. ... During production of mechanical components, residual dirt collects on*the*surfaces, thus creating a contamination that affects*the*durability of*the*assembled products. ... Note that*the**discretization*chosen*for**the*cylinders plays a big role in all*the*feature estimations, too. ...##
###
The Cheeger Constant, Isoperimetric Problems, and Hyperbolic Surfaces
[article]

2016
*
arXiv
*
pre-print

To do this, we use results of Hass-Morgan

arXiv:1509.08993v2
fatcat:xgvpvn3cnrhxpfe2ry64jlqgcu
*for**the**isoperimetric**problem*of these manifolds. We also give an example of a finite area 2-manifold where no such subset exists. ... We give a brief literature review of*the**isoperimetric**problem*and discuss its relationship with*the*Cheeger constant of Riemannian n-manifolds. ...*The*author would also like to thank his advisor Nathan Dunfield*for*suggesting this project as well as*for*many helpful suggestions and insights. ...##
###
On spanning tree congestion of graphs

2009
*
Discrete Mathematics
*

In this paper, we show

doi:10.1016/j.disc.2008.12.021
fatcat:rstajzdu7bh7rldhe7ruaxuaqu
*the*spanning tree congestion*for**the*complete k-partite graphs and*the*two-dimensional*tori*. ...*For*e ∈ E(T ),*the*congestion of e is*the*number of*edges*in G connecting two components of T − e.*The**edge*congestion of G in T is*the*maximum congestion over all*edges*in T . ... In Section 4, we show*the*spanning tree congestion*for**the*two-dimensional*tori*. This*problem*is related to Hruska's result*for**the*two-dimensional grids [12] . ...##
###
Page 4844 of Mathematical Reviews Vol. , Issue 2001G
[page]

2001
*
Mathematical Reviews
*

Summary: “We study

*the**problem*of partitioning point sets in*the*space so that each equivalence class is a convex polytope disjoint from*the*others.*For*a set of m points P in R? ...*The*lower bound also holds*for*partitions into empty convex CONVEX AND*DISCRETE*GEOMETRY polytopes.” ...
« Previous

*Showing results 1 — 15 out of 180 results*