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dc.contributor.authorBrignall, R
dc.contributor.authorRuskuc, Nik
dc.contributor.authorVatter, V
dc.date.accessioned2011-09-02T13:27:55Z
dc.date.available2011-09-02T13:27:55Z
dc.date.issued2011-07
dc.identifier5160265
dc.identifierc58a17af-679c-490f-bcb2-a37008630e07
dc.identifier80053077011
dc.identifier.citationBrignall , R , Ruskuc , N & Vatter , V 2011 , ' Simple extensions of combinatorial structures ' , Mathematika , vol. 57 , no. 2 , pp. 193-214 . https://doi.org/10.1112/S0025579310001518en
dc.identifier.issn0025-5793
dc.identifier.otherORCID: /0000-0003-2415-9334/work/73702074
dc.identifier.urihttps://hdl.handle.net/10023/1997
dc.description.abstractAn 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.
dc.format.extent213287
dc.language.isoeng
dc.relation.ispartofMathematikaen
dc.subjectQA Mathematicsen
dc.subject.lccQAen
dc.titleSimple extensions of combinatorial structuresen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doi10.1112/S0025579310001518
dc.description.statusPeer revieweden
dc.identifier.grantnumberGR/S53503/01en


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