Corpus ID: 9848465

On the Dimension and Euler characteristic of random graphs

@article{Knill2011OnTD,
  title={On the Dimension and Euler characteristic of random graphs},
  author={O. Knill},
  journal={ArXiv},
  year={2011},
  volume={abs/1112.5749}
}
  • O. Knill
  • Published 2011
  • Mathematics, Computer Science
  • ArXiv
  • The inductive dimension dim(G) of a finite undirected graph G=(V,E) is a rational number defined inductively as 1 plus the arithmetic mean of the dimensions of the unit spheres dim(S(x)) at vertices x primed by the requirement that the empty graph has dimension -1. We look at the distribution of the random variable "dim" on the Erdos-Renyi probability space G(n,p), where each of the n(n-1)/2 edges appears independently with probability p. We show here that the average dimension E[dim] is a… CONTINUE READING
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