Name
Abstract | ||
|---|---|---|
It is not hard to write a first order formula which is true for a given graph G but is false for any graph not isomorphic to G. The smallest number D(G) of nested quantifiers in such a formula can serve as a measure for the “first order complexity” of G. Here, this parameter is studied for random graphs. We determine it asymptotically when the edge probability p is constant; in fact, D(G) is of order log n then. For very sparse graphs its magnitude is &THgr;(n). On the other hand, for certain (carefully chosen) values of p the parameter D(G) can drop down to the very slow growing function log* n, the inverse of the TOWER-function. The general picture, however, is still a mystery. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2005 |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1002/rsa.v26:1/2 | Random Struct. Algorithms |
Keywords | Field | DocType |
random graph,function log,sparse graph,edge probability p,order complexity,parameter d,graph g,order logic,inc. random struct,order log n,order formula,first order logic,first order | Inverse,Random regular graph,Discrete mathematics,Binary logarithm,Combinatorics,Random graph,First-order logic,Isomorphism,Null model,Pathwidth,Mathematics | Journal |
Volume | Issue | ISSN |
26 | 1-2 | 1042-9832 |
Citations | PageRank | References |
9 | 0.77 | 5 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jeong Han Kim | 1 | 699 | 60.19 |
| Oleg Pikhurko | 2 | 318 | 47.03 |
| Joel H. Spencer | 3 | 200 | 54.20 |
| Oleg Verbitsky | 4 | 191 | 27.50 |