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Results tagged with random-graphs
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user 11540
The study of probability distributions over graphs. For example, the Erdős–Rényi model where each edge occurs independently with equal probability.
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Accepted
Can we estimate the probability $\mathbf{P}(a-k|a - b) $ on a random graph?
If you're willing to take $n$ large then we can use some known results about the "giant component," since the asymptotic situation is a good approximation to reality. Here is a paper by Erdos and Reny …
- 30.3k
1
vote
Survey/references on random geometric $K$-NN – $K$-nearest-neighbour graphs?
The wikipedia article on random geometric graphs only scratches the surface. A much deeper treatment is provided in Mathew Penrose's amazing text Random Geometric Graphs. Chapter 4 contains a treatmen …
- 30.3k
8
votes
Expected number of connected components in a random graph
Have a look at Chapter 11 of Alon and Spencer's The Probabilistic Method. They focus entirely on the case $p = \Theta(1/n)$, and the smallest p they consider is of the form $c/n$, which perhaps counts …
- 30.3k
1
vote
Finding an easy example applying the general Lovász local lemma
One of my favorite sources when I was learning about the local lemma was Notes on Randomized Algorithms by James Aspnes. There, the general local lemma from the OP is Lemma 11.3.1. In Sec 11.3.3, Aspn …
- 30.3k
4
votes
What is this Ramsey problem?
A good reference is Radziszowski's article Small Ramsey Numbers, which gets updated as new results are proven. In particular, this refers to basically all known Ramsey style results. The ones you're i …
- 30.3k