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The First Order Definability of Graphs: Upper Bounds for Quantifier Depth

By Oleg Verbitsky Helmut Veith Oleg Pikhurko

Abstract

... In passing we establish an upper bound for a related number D(G, G0), the minimum quantifier depth of a first order sentence which is true on exactly one of graphs G and G0. If G and G0 are non-isomorphic and both have n vertices, then D(G, G0) < = (n + 3)/2. This bound is tight up to an additive constant of 1. If we additionally require that a sentence distinguishing G and G0 is existential, we prove only a slightly weaker bound D(G, G0) < = (n + 5)/2

Topics: 1
Year: 2009
OAI identifier: oai:CiteSeerX.psu:10.1.1.135.4248
Provided by: CiteSeerX
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