On z-analogue of Stepanov-Lomonosov-Polesskii inequality

Authors:
Boris Pittel
Affiliations:
-
Venue:
Journal of Combinatorial Theory Series B
Year:
2013

Citing 5
Cited 0

A generaliztion of an inequality of Stepanov

Journal of Combinatorial Theory Series B
Counting connected graphs inside-out

Journal of Combinatorial Theory Series B
Counting connected graphs asymptotically

European Journal of Combinatorics - Special issue on extremal and probabilistic combinatorics
Large-deviations/thermodynamic approach to percolation on the complete graph

Random Structures & Algorithms
Corrigendum: Corrigendum to “Counting connected graphs inside-out” [J. Combin. Theory Ser. B 93 (2005) 127--172]

Journal of Combinatorial Theory Series B

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Abstract

Stepanov@?s 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.