Spanning subgraphs of random graphs

1992 ◽  
Vol 8 (1) ◽  
pp. 91-94 ◽  
Author(s):  
Noga Alon ◽  
Zolt�n F�redi
Keyword(s):  
Random Graphs ◽  
Spanning Subgraphs

scholarly journals Almost spanning subgraphs of random graphs after adversarial edge removal

2009 ◽  
Vol 35 ◽  
pp. 335-340 ◽  
Author(s):  
Julia Böttcher ◽  
Yoshiharu Kohayakawa ◽  
Anusch Taraz
Keyword(s):  
Random Graphs ◽  
Spanning Subgraphs ◽  
Edge Removal

Spanning Subgraphs of Random Graphs

2000 ◽  
Vol 9 (2) ◽  
pp. 125-148 ◽  
Author(s):  
OLIVER RIORDAN
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Moment Method ◽  
Subgraph Isomorphic ◽  
Square Grid ◽  
Spanning Subgraphs ◽  
Spanning Subgraph ◽  
Fixed Probability ◽  
Second Moment Method ◽  
The Second Moment Method

Let Gp be a random graph on 2d vertices where edges are selected independently with a fixed probability p > ¼, and let H be the d-dimensional hypercube Qd. We answer a question of Bollobás by showing that, as d → ∞, Gp almost surely has a spanning subgraph isomorphic to H. In fact we prove a stronger result which implies that the number of d-cubes in G ∈ [Gscr ](n, M) is asymptotically normally distributed for M in a certain range. The result proved can be applied to many other graphs, also improving previous results for the lattice, that is, the 2-dimensional square grid. The proof uses the second moment method – writing X for the number of subgraphs of G isomorphic to H, where G is a suitable random graph, we expand the variance of X as a sum over all subgraphs of H itself. As the subgraphs of H may be quite complicated, most of the work is in estimating the various terms of this sum.

scholarly journals Local resilience of spanning subgraphs in sparse random graphs

2015 ◽  
Vol 49 ◽  
pp. 513-521 ◽  
Author(s):  
Peter Allen ◽  
Julia Böttcher ◽  
Julia Ehrenmüller ◽  
Anusch Taraz
Keyword(s):  
Random Graphs ◽  
Spanning Subgraphs ◽  
Local Resilience

scholarly journals Almost Spanning Subgraphs of Random Graphs After Adversarial Edge Removal

2013 ◽  
Vol 22 (5) ◽  
pp. 639-683 ◽  
Author(s):  
JULIA BÖTTCHER ◽  
YOSHIHARU KOHAYAKAWA ◽  
ANUSCH TARAZ
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Maximum Degree ◽  
Bipartite Graphs ◽  
Fixed Integer ◽  
Spanning Subgraphs ◽  
Edge Removal

Let Δ ≥ 2 be a fixed integer. We show that the random graph${\mathcal{G}_{n,p}}$with$p\gg (\log n/n)^{1/\Delta}$is robust with respect to the containment of almost spanning bipartite graphsHwith maximum degree Δ and sublinear bandwidth in the following sense: asymptotically almost surely, if an adversary deletes arbitrary edges from${\mathcal{G}_{n,p}}$in such a way that each vertex loses less than half of its neighbours, then the resulting graph still contains a copy of all suchH.

Random Graphs

1998 ◽  
Author(s):  
V. F. Kolchin
Keyword(s):  
Random Graphs

Enumerating Highly-Edge-Connected Spanning Subgraphs

2019 ◽  
Vol E102.A (9) ◽  
pp. 1002-1006
Author(s):  
Katsuhisa YAMANAKA ◽  
Yasuko MATSUI ◽  
Shin-ichi NAKANO
Keyword(s):  
Spanning Subgraphs

Applications of random graphs

2017 ◽  
Author(s):  
A.C.C. Coolen ◽  
A. Annibale ◽  
E.S. Roberts
Keyword(s):  
Social Networks ◽  
Random Graphs ◽  
Interaction Network ◽  
Power Grids ◽  
Protein Protein Interaction ◽  
Topological Features ◽  
First Case ◽  
The Stability ◽  
Protein Protein Interaction Network

This chapter reviews graph generation techniques in the context of applications. The first case study is power grids, where proposed strategies to prevent blackouts have been tested on tailored random graphs. The second case study is in social networks. Applications of random graphs to social networks are extremely wide ranging – the particular aspect looked at here is modelling the spread of disease on a social network – and how a particular construction based on projecting from a bipartite graph successfully captures some of the clustering observed in real social networks. The third case study is on null models of food webs, discussing the specific constraints relevant to this application, and the topological features which may contribute to the stability of an ecosystem. The final case study is taken from molecular biology, discussing the importance of unbiased graph sampling when considering if motifs are over-represented in a protein–protein interaction network.

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