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Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/1997
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Title: Simple extensions of combinatorial structures
Authors: Brignall, R
Ruskuc, Nik
Vatter, V
Keywords: QA Mathematics
Issue Date: Jul-2011
Citation: Brignall , R , Ruskuc , N & Vatter , V 2011 , ' Simple extensions of combinatorial structures ' Mathematika , vol 57 , no. 2 , pp. 193-214 .
Abstract: An interval in a combinatorial structure R is a set I of points which are related to every point in R \ I in the same way. A structure is simple if it has no proper intervals. Every combinatorial structure can be expressed as an inflation of a simple structure by structures of smaller sizes — this is called the substitution (or modular) decomposition. In this paper we prove several results of the following type: An arbitrary structure S of size n belonging to a class C can be embedded into a simple structure from C by adding at most f (n) elements. We prove such results when C is the class of all tournaments, graphs, permutations, posets, digraphs, oriented graphs and general relational structures containing a relation of arity greater than 2. The function f (n) in these cases is 2, ⌈log2(n + 1)⌉, ⌈(n + 1)/2⌉, ⌈(n + 1)/2⌉, ⌈log4(n + 1)⌉, ⌈log3(n + 1)⌉ and 1, respectively. In each case these bounds are the best possible.
Version: Preprint
Status: Peer reviewed
URI: http://hdl.handle.net/10023/1997
DOI: http://dx.doi.org/10.1112/S0025579310001518
ISSN: 0025-5793
Type: Journal article
Rights: This is the author's version of the article, which may be different to the published version. The published version copyright (c) University College London 2010 is available from http://journals.cambridge.org
Appears in Collections:University of St Andrews Research
Pure Mathematics Research



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