Existence of μ-representation of graphs
Kitaev, Sergey (2017) Existence of μ-representation of graphs. Journal of Graph Theory, 85 (3). pp. 661-668. ISSN 1097-0118
|
Text (Kitaev-JGT2016-Existence-of-μ-representation-of-graphs)
Kitaev_JGT2016_Existence_of_representation_of_graphs.pdf - Accepted Author Manuscript Download (77kB) | Preview |
Abstract
Recently, Jones et al. introduced the study of μ-representable graphs, where μ is a word over { 1,2} containing at least one 1. The notion of a μ-representable graph is a far-reaching generalization of the notion of a word-representable graph studied in the literature in a series of papers. Jones et al. have shown that any graph is 11⋯1-representable assuming that the number of 1s is at least three, while the class of 12-rerpesentable graphs is properly contained in the class of comparability graphs, which, in turn, is properly contained in the class of word-representable graphs corresponding to 11-representable graphs. Further studies in this direction were conducted by Nabawanda, who has shown, in particular, that the class of 112-representable graphs is not included in the class of word-representable graphs. Jones et al. raised a question on classification of μ-representable graphs at least for small values of μ. In this paper we show that if μ is of length at least 3 then any graph is μ-representable. This rather unexpected result shows that from existence of representation point of view there are only two interesting non-equivalent cases in the theory of μ-representable graphs, namely, those of μ=11 and μ=12.
| Item type: | Article |
|---|---|
| ID code: | 57302 |
| Notes: | This is the accepted version of the following article: Kitaev, S. (2016). Existence of μ-representation of graphs. Journal of Graph Theory. which has been published in final form at http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0118 . This article may be used for non-commercial purposes in accordance with the Wiley Self-Archiving Policy [http://olabout.wiley.com/WileyCDA/Section/id-828039.html]. |
| Keywords: | μ-representable graph, pattern matching, pattern avoidance, word-representable graphs, Mathematics, Mathematics(all) |
| Subjects: | Science > Mathematics |
| Department: | Faculty of Science > Computer and Information Sciences |
| Depositing user: | Pure Administrator |
| Date deposited: | 05 Aug 2016 13:42 |
| Last modified: | 16 Oct 2017 09:12 |
| Related URLs: | |
| URI: | https://strathprints.strath.ac.uk/id/eprint/57302 |
| Export data: |
CORE (COnnecting REpositories)
CORE (COnnecting REpositories)