Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4656944 | Journal of Combinatorial Theory, Series B | 2013 | 10 Pages |
Abstract
Stepanovʼs inequality and its various extensions provide an upper bound for connectedness probability for a Bernoulli-type random subgraph of a given graph. We have found an analogue of this bound for the expected value of the connectedness-event indicator times a positive z raised to the number of edges in the random subgraph. We demonstrate the power of this bound by a quick derivation of a relatively sharp bound for the number of the spanning connected, sparsely edged, subgraphs of a high-degree regular graph.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Boris Pittel,