scholarly journals POISSON APPROXIMATION FOR THE NUMBER OF INDUCED COPIES OF A FIXED GRAPH IN A RANDOM REGULAR GRAPH

2014 ◽  
Vol 95 (1) ◽  
Author(s):  
M. Donganont
Keyword(s):  
Regular Graph ◽  
Poisson Approximation ◽  
Random Regular Graph

scholarly journals Optimal Construction of Edge-Disjoint Paths in Random Regular Graphs

2000 ◽  
Vol 9 (3) ◽  
pp. 241-263 ◽  
Author(s):  
ALAN M. FRIEZE ◽  
LEI ZHAO
Keyword(s):  
Polynomial Time ◽  
Regular Graph ◽  
Randomized Algorithm ◽  
Constant Factor ◽  
Disjoint Paths ◽  
Regular Graphs ◽  
Edge Disjoint ◽  
Random Regular Graph ◽  
Arbitrary Graphs ◽  
Optimal Construction

Given a graph G = (V, E) and a set of κ pairs of vertices in V, we are interested in finding, for each pair (ai, bi), a path connecting ai to bi such that the set of κ paths so found is edge-disjoint. (For arbitrary graphs the problem is [Nscr ][Pscr ]-complete, although it is in [Pscr ] if κ is fixed.)We present a polynomial time randomized algorithm for finding edge-disjoint paths in the random regular graph Gn,r, for sufficiently large r. (The graph is chosen first, then an adversary chooses the pairs of end-points.) We show that almost every Gn,r is such that all sets of κ = Ω(n/log n) pairs of vertices can be joined. This is within a constant factor of the optimum.

scholarly journals Expansion properties of a random regular graph after random vertex deletions

2008 ◽  
Vol 29 (5) ◽  
pp. 1139-1150 ◽  
Author(s):  
Catherine Greenhill ◽  
Fred B. Holt ◽  
Nicholas Wormald
Keyword(s):  
Regular Graph ◽  
Random Regular Graph

Induced Subgraph in Random Regular Graph

2008 ◽  
Vol 21 (4) ◽  
pp. 645-650
Author(s):  
Lan XIAO ◽  
Guiying YAN ◽  
Yuwen WU ◽  
Wei REN
Keyword(s):  
Regular Graph ◽  
Induced Subgraph ◽  
Random Regular Graph

scholarly journals Dismantling Sparse Random Graphs

2008 ◽  
Vol 17 (2) ◽  
pp. 259-264 ◽  
Author(s):  
SVANTE JANSON ◽  
ANDREW THOMASON
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Regular Graph ◽  
Random Regular Graph

We consider the number of vertices that must be removed from a graphGin order that the remaining subgraph have no component with more thankvertices. Our principal observation is that, ifGis a sparse random graph or a random regular graph onnvertices withn→ ∞, then the number in question is essentially the same for all values ofkthat satisfy bothk→ ∞ andk=o(n).

scholarly journals Return probability for the Anderson model on the random regular graph

2018 ◽  
Vol 98 (13) ◽  
Author(s):  
Soumya Bera ◽  
Giuseppe De Tomasi ◽  
Ivan M. Khaymovich ◽  
Antonello Scardicchio
Keyword(s):  
Regular Graph ◽  
Anderson Model ◽  
Return Probability ◽  
Random Regular Graph

Bootstrap percolation on the random regular graph

2006 ◽  
Vol 30 (1-2) ◽  
pp. 257-286 ◽  
Author(s):  
József Balogh ◽  
Boris G. Pittel
Keyword(s):  
Regular Graph ◽  
Bootstrap Percolation ◽  
Random Regular Graph

scholarly journals The Cover Time of a Biased Random Walk on a Random Regular Graph of Odd Degree

10.37236/8327 ◽  
2020 ◽  
Vol 27 (4) ◽  
Author(s):  
Tony Johansson
Keyword(s):  
Random Walk ◽  
Regular Graph ◽  
Vertex Cover ◽  
Random Walk Process ◽  
Cover Time ◽  
Edge Cover ◽  
Biased Random Walk ◽  
Random Regular Graph ◽  
Odd Degree ◽  
Leading Term

We consider a random walk process on graphs introduced by Orenshtein and Shinkar (2014). At any time, the random walk moves from its current position along a previously unvisited edge chosen uniformly at random, if such an edge exists. Otherwise, it walks along a previously visited edge chosen uniformly at random. For the random $r$-regular graph, with $r$ a constant odd integer, we show that this random walk process has asymptotic vertex and edge cover times $\frac{1}{r-2}n\log n$ and $\frac{r}{2(r-2)}n\log n$, respectively, generalizing a result of Cooper, Frieze and the author (2018) from $r = 3$ to any odd $r\geqslant 3$. The leading term of the asymptotic vertex cover time is now known for all fixed $r\geqslant 3$, with Berenbrink, Cooper and Friedetzky (2015) having shown that $G_r$ has vertex cover time asymptotic to $\frac{rn}{2}$ when $r\geqslant 4$ is even.

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