Files in this item
Simple extensions of combinatorial structures
Item metadata
dc.contributor.author | Brignall, R | |
dc.contributor.author | Ruskuc, Nik | |
dc.contributor.author | Vatter, V | |
dc.date.accessioned | 2011-09-02T13:27:55Z | |
dc.date.available | 2011-09-02T13:27:55Z | |
dc.date.issued | 2011-07 | |
dc.identifier | 5160265 | |
dc.identifier | c58a17af-679c-490f-bcb2-a37008630e07 | |
dc.identifier | 80053077011 | |
dc.identifier.citation | Brignall , R , Ruskuc , N & Vatter , V 2011 , ' Simple extensions of combinatorial structures ' , Mathematika , vol. 57 , no. 2 , pp. 193-214 . https://doi.org/10.1112/S0025579310001518 | en |
dc.identifier.issn | 0025-5793 | |
dc.identifier.other | ORCID: /0000-0003-2415-9334/work/73702074 | |
dc.identifier.uri | https://hdl.handle.net/10023/1997 | |
dc.description.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. | |
dc.format.extent | 213287 | |
dc.language.iso | eng | |
dc.relation.ispartof | Mathematika | en |
dc.subject | QA Mathematics | en |
dc.subject.lcc | QA | en |
dc.title | Simple extensions of combinatorial structures | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | 10.1112/S0025579310001518 | |
dc.description.status | Peer reviewed | en |
dc.identifier.grantnumber | GR/S53503/01 | en |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.