scholarly journals Cover time of a random graph with a degree sequence II: Allowing vertices of degree two

2014 ◽  
Vol 45 (4) ◽  
pp. 627-674
Author(s):  
Colin Cooper ◽  
Alan Frieze ◽  
Eyal Lubetzky
Keyword(s):  
Random Graph ◽  
Degree Sequence ◽  
Cover Time

scholarly journals Cover time of a random graph with given degree sequence

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Mohammed Abdullah ◽  
Colin Cooper ◽  
Alan Frieze
Keyword(s):  
Random Graph ◽  
High Probability ◽  
Minimum Degree ◽  
Degree Sequence ◽  
Average Degree ◽  
Cover Time ◽  
Vertex Set ◽  
International Audience

International audience In this paper we establish the cover time of a random graph $G(\textbf{d})$ chosen uniformly at random from the set of graphs with vertex set $[n]$ and degree sequence $\textbf{d}$. We show that under certain restrictions on $\textbf{d}$, the cover time of $G(\textbf{d})$ is with high probability asymptotic to $\frac{d-1}{ d-2} \frac{\theta}{ d}n \log n$. Here $\theta$ is the average degree and $d$ is the $\textit{effective minimum degree}$. The effective minimum degree is the first entry in the sorted degree sequence which occurs order $n$ times.

scholarly journals Cover time of a random graph with given degree sequence

2012 ◽  
Vol 312 (21) ◽  
pp. 3146-3163 ◽  
Author(s):  
Mohammed Abdullah ◽  
Colin Cooper ◽  
Alan Frieze
Keyword(s):  
Random Graph ◽  
Degree Sequence ◽  
Cover Time

The cover time of the giant component of a random graph

2008 ◽  
Vol 32 (4) ◽  
pp. 401-439 ◽  
Author(s):  
Colin Cooper ◽  
Alan Frieze
Keyword(s):  
Random Graph ◽  
Giant Component ◽  
Cover Time

scholarly journals A Note on the Warmth of Random Graphs with Given Expected Degrees

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Statistical Mechanics ◽  
Chromatic Number ◽  
Random Graph ◽  
Lower Bounds ◽  
Random Graphs ◽  
Upper Bound ◽  
Degree Sequence ◽  
Graph Model ◽  
Upper And Lower Bounds ◽  
Random Graph Model

We consider the random graph modelG(w)for a given expected degree sequencew=(w1,w2,…,wn). Warmth, introduced by Brightwell and Winkler in the context of combinatorial statistical mechanics, is a graph parameter related to lower bounds of chromatic number. We present new upper and lower bounds on warmth ofG(w). In particular, the minimum expected degree turns out to be an upper bound of warmth when it tends to infinity and the maximum expected degreem=O(nα)with0<α<1/2.

scholarly journals The number of graphs and a random graph with a given degree sequence

2012 ◽  
Vol 42 (3) ◽  
pp. 301-348 ◽  
Author(s):  
Alexander Barvinok ◽  
J.A. Hartigan
Keyword(s):  
Random Graph ◽  
Degree Sequence

scholarly journals On the Degree Sequence of an Evolving Random Graph Process and Its Critical Phenomenon

2009 ◽  
Vol 46 (4) ◽  
pp. 1213-1220 ◽  
Author(s):  
Xian-Yuan Wu ◽  
Zhao Dong ◽  
Ke Liu ◽  
Kai-Yuan Cai
Keyword(s):  
Random Graph ◽  
Degree Distribution ◽  
Critical Phenomenon ◽  
Degree Sequence ◽  
Edge Deletion ◽  
Specific Parameter

In this paper we focus on the problem of the degree sequence for a random graph process with edge deletion. We prove that, while a specific parameter varies, the limit degree distribution of the model exhibits critical phenomenon.

scholarly journals Phase transition on the degree sequence of a random graph process with vertex copying and deletion

2011 ◽  
Vol 121 (4) ◽  
pp. 885-895 ◽  
Author(s):  
Kai-Yuan Cai ◽  
Zhao Dong ◽  
Ke Liu ◽  
Xian-Yuan Wu
Keyword(s):  
Phase Transition ◽  
Random Graph ◽  
Degree Sequence

scholarly journals The scaling window for a random graph with a given degree sequence

2012 ◽  
Vol 41 (1) ◽  
pp. 99-123 ◽  
Author(s):  
Hamed Hatami ◽  
Michael Molloy
Keyword(s):  
Random Graph ◽  
Degree Sequence ◽  
Scaling Window
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