Radius and diameter of random subgraphs of the hypercube

1993 ◽  
Vol 4 (2) ◽  
pp. 215-229 ◽  
Author(s):  
A. V. Kostochka ◽  
A. A. Sapozhenko ◽  
K. Weber
Keyword(s):  
Random Subgraphs

scholarly journals Random subgraphs of finite graphs: I. The scaling window under the triangle condition

2005 ◽  
Vol 27 (2) ◽  
pp. 137-184 ◽  
Author(s):  
Christian Borgs ◽  
Jennifer T. Chayes ◽  
Remco van der Hofstad ◽  
Gordon Slade ◽  
Joel Spencer
Keyword(s):  
Finite Graphs ◽  
Triangle Condition ◽  
Scaling Window ◽  
Random Subgraphs

scholarly journals Random subgraphs of the n-cycle and the n-wheel

1991 ◽  
Vol 93 (1) ◽  
pp. 35-53 ◽  
Author(s):  
Wojciech Kordecki
Keyword(s):  
N Cycle ◽  
Random Subgraphs

Distances in Random Induced Subgraphs of Generalized n-Cubes

2002 ◽  
Vol 11 (6) ◽  
pp. 599-605 ◽  
Author(s):  
C. M. REIDYS
Keyword(s):  
Direct Product ◽  
Finite Alphabet ◽  
Complete Graphs ◽  
Induced Subgraphs ◽  
Induced Subgraph ◽  
Random Subgraphs ◽  
Independent Probability

In this paper we study distances in random subgraphs of a generalized n-cube [Qscr ]ns over a finite alphabet S of size s. [Qscr ]ns is the direct product of complete graphs over s vertices, its vertices being the n-tuples (x1, …, xn), with xi ∈ S, i = 1, … n, and two vertices being adjacent if they differ in exactly one coordinate. A random (induced) subgraph γ of [Qscr ]ns is obtained by selecting [Qscr ]ns-vertices with independent probability pn and then inducing the corresponding edges from [Qscr ]ns. Our main result is that dγ (P,Q) [les ] [2k+3]d[Qscr ]ns (P,Q) almost surely for P,Q ∈ γ, pn = n−a and 0 [les ] a < ½, where k = [1+3a/1−2a] and dγ and d[Qscr ]ns denote the distances in γ and [Qscr ]ns, respectively.

scholarly journals Random Subgraphs in Sparse Graphs

2015 ◽  
Vol 29 (4) ◽  
pp. 2350-2360
Author(s):  
Felix Joos
Keyword(s):  
Sparse Graphs ◽  
Random Subgraphs

scholarly journals Random Subgraphs Of Finite Graphs: III. The Phase Transition For The n-Cube

COMBINATORICA ◽  
2006 ◽  
Vol 26 (4) ◽  
pp. 395-410 ◽  
Author(s):  
Christian Borgs ◽  
Jennifer T. Chayes ◽  
Remco van der Hofstad ◽  
Gordon Slade ◽  
Joel Spencer
Keyword(s):  
Phase Transition ◽  
Finite Graphs ◽  
Random Subgraphs

scholarly journals Random subgraphs of finite graphs. II. The lace expansion and the triangle condition

2005 ◽  
Vol 33 (5) ◽  
pp. 1886-1944 ◽  
Author(s):  
Christian Borgs ◽  
Jennifer T. Chayes ◽  
Remco van der Hofstad ◽  
Gordon Slade ◽  
Joel Spencer
Keyword(s):  
Lace Expansion ◽  
Finite Graphs ◽  
Triangle Condition ◽  
Random Subgraphs
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