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

##
###
Connectivity properties of random subgraphs of the cube

1995
*
Random structures & algorithms (Print)
*

Thus Q t is a spanning

doi:10.1002/rsa.3240060210
fatcat:zzhjjyi7frb4xmufshwrgurff4
*subgraph**of*Q n*of*size t, and Q t is obtained from Q t−1 by*the**random*addition*of*an edge*of*Q n not in Q t−1 . ... Clearly Q n is an n-*connected*graph*of*diameter and radius n. Write M = n2 n−1 = e(Q n ) for*the*size*of*Q n . Let Q = (Q t ) M 0 be a*random*Q n -process. ... Part*of*this work was done while*the*first and*the*third authors were visiting*the*Instituto de Matemática e Estatística, Universidade de São Paulo. ...##
###
Page 4037 of Mathematical Reviews Vol. , Issue 2003f
[page]

2003
*
Mathematical Reviews
*

This class coincides with that

*of*partial*cubes*, and has*the**property*that*the*edges belonging to each 6@-class F form a matching, and G~ F consists*of*exactly two*connected*components [P. M. ... Important results are as follows: (i) Every graph is*the*crossing graph*of*some median graph; (ii) a partial*cube*G is bi-*connected*if and only if G# is*connected*; (iii) a partial*cube*has a triangle- ...##
###
Page 6639 of Mathematical Reviews Vol. , Issue 92m
[page]

1992
*
Mathematical Reviews
*

Zbigniew Palka (PL-POZN)
92m:05167 05C80 Bollobas, B. (4-CAMB); Kohayakawa, Y. (4-CAMB); Luczak, T. (4-CAMB)

*The*evolution*of**random**subgraphs**of**the**cube*. ...*Random*Structures Algorithms 3 (1992), no. 1, 55-90. This paper presents*the*results*of*detailed studies*of**the*critical phase*of**the*evolution*of*a*random**cube*. ...##
###
On the Largest Eigenvalue of a Random Subgraph of the Hypercube

2003
*
Communications in Mathematical Physics
*

Let G be a

doi:10.1007/s00220-003-0872-y
fatcat:bjc27sf3nvbwxbkkagzischqhu
*random**subgraph**of**the*n-*cube*where each edge appears randomly and independently with probability p. ... We prove that*the*largest eigenvalue*of**the*adjacency matrix*of*G is almost surely λ_1(G)= (1+o(1)) max(Δ^1/2(G),np), where Δ(G) is*the*maximum degree*of*G and o(1) term tends to zero as max (Δ^1/2(G), ...*The*first author would like to thank Sergey Gavrilets and Janko Gravner for bringing this problem to his attention and for useful discussions. ...##
###
Page 2318 of Mathematical Reviews Vol. , Issue 86f
[page]

1986
*
Mathematical Reviews
*

G is a fixed

*connected*regular graph*of*order n with no triangles. A*random**subgraph*RG(p)*of*G is obtained by selecting its lines independently and with a common probability p. ...*The*author presents recent developments in*the*study*of*such*random*graphs.*The*main subjects covered are threshold functions*of*and*the*asymptotic distribution*of*various balanced*subgraphs*. ...##
###
Page 3 of Mathematical Reviews Vol. , Issue 93i
[page]

1993
*
Mathematical Reviews
*

theorem) and basic

*properties*such as first-order*properties*and*properties**of*large subsets*of*vertices. ... In*the*case*of*circular arc graphs, we show that every integral power*of*a circular arc graph is a circular arc graph.” 93i:05111 05C75 05E30 Weichsel, Paul M. (1-IL) Distance regular*subgraphs**of*a*cube*...##
###
Connecting boundary and interior - "Gauss's law" for graphs
[article]

2011
*
arXiv
*
pre-print

*The*Gauss's law, in an abstract sense, is a theorem that relates quantities on

*the*boundary (flux) to

*the*interior (charge)

*of*a surface. ... In this article, we try to construct a definition

*of*flux for other graphs, such that a similar boundary-interior relation can be satisfied. ... Szeto acknowledges

*the*support

*of*CERG602507 grant. ...

##
###
Random Induced Subgraphs of Generalizedn-Cubes

1997
*
Advances in Applied Mathematics
*

ACKNOWLEDGMENTS I gratefully acknowledge

doi:10.1006/aama.1997.0553
fatcat:bn2dwvm7wbewzmgsl6rm7kzgnu
*the*proofreading and help*of*W. Y. C. Chen and Q. H. Hou. Further I want to thank C. L. Barrett for many discussions. ... Finally,*the*threshold value for*the**connectivity**property*P, Q w x*of**random*induced*subgraphs*13, 11 is determined. ... Ž . vertices*of*Q Q are n-tuples x , . . . , x , where x g A A, i s 1, . . . , n, and two*The*main motivation for introducing*random*induced*subgraphs**of*generalized n-*cubes*, Q Q n , is*the*analysis*of*...##
###
Page 5481 of Mathematical Reviews Vol. , Issue 98I
[page]

1998
*
Mathematical Reviews
*

Summary: “

*The*subject*of*this paper is to analyse*connectivity*and paths in*random*induced*subgraphs**of*generalized n-*cubes*@" over an alphabet # with |./| = a. ... {For*the*entire collection see MR 98e:00009. } Martin Baéa (SK-KTU; KoSice) 98i:05146 05C80 Reidys, Christian M. (1-LANL; Los Alamos, NM)*Random*induced*subgraphs**of*generalized n-*cubes*. ...##
###
Page 6421 of Mathematical Reviews Vol. , Issue 91M
[page]

1991
*
Mathematical Reviews
*

Summary: “Dyer, Frieze and Foulds introduced a general model

*of**random**subgraphs*G,,*of**the*n-*cube*graph Q,. ... (DDR-SEE) On*the*radius*of**random**subgraphs**of**the*-*cube*. Topics in combinatorics and graph theory (Oberwolfach, 1990), 505-511, Physica, Heidelberg, 1990. ...##
###
Edge Expansion of Cubical Complexes
[article]

2005
*
arXiv
*
pre-print

In this paper we show that graphs

arXiv:math/0506478v1
fatcat:dzled3pwrvc3rdfh4g4tqkjwae
*of*"neighbourly" cubical complexes -- cubical complexes in which every pair*of*vertices spans a (unique)*cube*-- have good expansion*properties*, using a technique based ... By showing that graphs*of*stable set polytopes are graphs*of*neighbourly cubical complexes we give a new proof that graphs*of*stable set polytopes have edge expansion 1. ... Acknowledgements I thank Volker Kaibel for many helpful suggestions which led to a significantly simpler proof*of*Lemma 2.1. ...##
###
Fast Approximation Schemes for Euclidean Multi-connectivity Problems
[chapter]

2000
*
Lecture Notes in Computer Science
*

*The*efficiency

*of*our scheme relies on transformations

*of*nearly optimal low cost special spanners into sub-multigraphs having good decomposition and approximation

*properties*and a simple

*subgraph*

*connectivity*... Furthermore, by showing a low-cost transformation

*of*a k-edge

*connected*graph maintaining

*the*k-edge

*connectivity*and developing novel decomposition

*properties*, we derive a PTAS for Euclidean minimum-cost ... Acknowledgments We thank unknown referees for their valuable comments and suggestions (because

*of*space considerations not all

*of*

*the*suggestions could be implemented). ...

##
###
Virtually Fibering Right-Angled Coxeter Groups
[article]

2017
*
arXiv
*
pre-print

*The*proof uses Bestvina-Brady Morse theory facilitated by combinatorial arguments. We describe a variety

*of*examples where

*the*plan succeeds or fails. ... Among

*the*successful examples are

*the*right-angled reflection groups in H^4 with fundamental domain

*the*120-cell or

*the*24-cell. ... Its vertex-face incidence graph VF(Θ) has

*the*

*property*that any proper

*connected*

*subgraph*with κ ≥ 0 is a square or a chain

*of*length ≤ 2. ...

##
###
Page 4156 of Mathematical Reviews Vol. , Issue 92h
[page]

1992
*
Mathematical Reviews
*

(D-SEFA)
On

*the*diameter*of**random**subgraphs**of**the*n-*cube*. Contemporary methods in graph theory, 507-524, Bibliographisches Inst., Mannheim, 1990. ... Let G, = (Vn, En) be a*subgraph**of**the*n-*cube*Q” where V,, is randomly sampled from*the*vertex set*of*Q” so that P(x € V,) = Py independently*of*all other vertices and E,, is randomly sampled from*the*...##
###
Page 4959 of Mathematical Reviews Vol. , Issue 94i
[page]

1994
*
Mathematical Reviews
*

We derive bounds on

*the*relationship between size and depth for*the*components*of*a nearest-neighbor graph and prove some proba- bilistic*properties**of**the*k-nearest-neighbors graph for a*random*set*of*...*The*authors say that they have been able to use*the*same tech- nique also to obtain NP-completeness results for restricted families*of*graphs, such as induced*subgraphs**of**the**cube*or trees. ...
« Previous

*Showing results 1 — 15 out of 4,214 results*