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4 votes
1 answer
566 views

Random graphs and Benjamini-Schramm convergence

I am looking for literature on the question whether a randomly chosen sequence of $k$-regular graphs converges in the Benjamini-Schramm sense to the universal covering with probability one. There are ...
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0 votes
0 answers
320 views

Gromov-Hausdorff distance measure between minimum spanning trees

I am trying to compare minimum spanning trees through time. I have two questions: 1-Is it possible to measure the similarity between two minimum spanning trees with Gromov-Hausdorff distance measure ...
Sam's user avatar
  • 1
8 votes
1 answer
314 views

Longest induced cycles in random geometric graphs near criticality

We make a random geometric graph $X(n;r)$ as follows. Choose $n$ points uniformly, independently, in the unit square $[0,1]^2$, for vertices, and then connect a pair of vertices $\{ p,q \}$ by an edge ...
Matthew Kahle's user avatar
4 votes
2 answers
882 views

The probability distribution for vertex degree in a unit disc graph generated from random points on a plane

Imagine I cover an arbitrarily large plane with randomly placed points at some density $\rho$ s.t. the number of points in any randomly sampled area $A$ (of arbitrary shape and size) is $\approx A*\...
FloatingLantern's user avatar