RANDOM GRAPH ORDERS DO NOT SATISFY A 0-1-LAW

Authors
BRIGHTWELL G
Citation
G. Brightwell, RANDOM GRAPH ORDERS DO NOT SATISFY A 0-1-LAW, Random structures & algorithms, 6(2-3), 1995, pp. 231-237
Citations number
16
Categorie Soggetti
Mathematics,Mathematics,Mathematics,"Computer Science Software Graphycs Programming
Journal title
Random structures & algorithms → ACNP
ISSN journal
10429832
Volume
6
Issue
2-3
Year of publication
1995
Pages
231 - 237
Database
ISI
SICI code
1042-9832(1995)6:2-3<231:RGODNS>2.0.ZU;2-W
Abstract
The random graph order P-n,P-p is defined by taking a random graph G(n ,p) on vertex set [n], interpreting an edge between vertices i and j, with i < j in [n], as a relation i < j, and taking the transitive clos ure. We present a first-order property Q of P-n,P-p such that the limi ting probability of Q is bounded away from both 0 and 1 as n-->infinit y, whenever pn is bounded away from 0 and p is bounded away from 1. (C ) 1995 John Wiley & Sons, Inc.