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First order zero–one laws for random graphs on the circle
Author(s) -
McColm Gregory L.
Publication year - 1999
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/(sici)1098-2418(199905)14:3<239::aid-rsa3>3.0.co;2-3
Subject(s) - random graph , zero (linguistics) , mathematics , struct , combinatorics , order (exchange) , discrete mathematics , graph , space (punctuation) , metric space , computer science , philosophy , linguistics , finance , economics , programming language , operating system
We look at a competitor of the Erdős–Rényi models of random graphs, one proposed in E. Gilbert [J. Soc. Indust. Appl. Math. 9:4, 533–543 (1961)]: given δ>0 and a metric space X of diameter >δ, scatter n vertices at random on X and connect those of distance <δ apart: we get a random graph G n , δ X . Letting X be a circle, we look at zero‐one laws for (in First Order Logic) various δ. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 239–266, 1999