On z-analogue of Stepanov–Lomonosov–Polesskii inequality |
| |
Authors: | Boris Pittel |
| |
Institution: | Ohio State University, Columbus, OH, USA |
| |
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. |
| |
Keywords: | Random graphs Connectedness Directed Enumeration Martingale Bounds |
本文献已被 ScienceDirect 等数据库收录! |
|