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Properties of Classes of Random Graphs

Published online by Cambridge University Press:  12 September 2008

Neal Brand  and
Steve Jackson
Neal Brand
Affiliation:
Department of Mathematics, University of North Texas, Denton, TX 76203, USA
Steve Jackson
Affiliation:
Department of Mathematics, University of North Texas, Denton, TX 76203, USA
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Abstract

In [11] it is shown that the theory of almost all graphs is first-order complete. Furthermore, in [3] a collection of first-order axioms are given from which any first-order property or its negation can be deduced. Here we show that almost all Steinhaus graphs satisfy the axioms of almost all graphs and conclude that a first-order property is true for almost all graphs if and only if it is true for almost all Steinhaus graphs. We also show that certain classes of subgraphs of vertex transitive graphs are first-order complete. Finally, we give a new class of higher-order axioms from which it follows that large subgraphs of specified type exist in almost all graphs.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 4 , December 1994 , pp. 435 - 454
Copyright
Copyright © Cambridge University Press 1994

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