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dc.contributor.authorAkgün, Özgür
dc.contributor.authorGent, Ian P.
dc.contributor.authorKitaev, Sergey
dc.contributor.authorZantema, Hans
dc.identifier.citationAkgün , Ö , Gent , I P , Kitaev , S & Zantema , H 2019 , ' Solving computational problems in the theory of word-representable graphs ' , Journal of Integer Sequences , vol. 22 , no. 2 , 19.2.5 . < >en
dc.identifier.otherPURE: 258221847
dc.identifier.otherPURE UUID: 6d13ed10-041c-43c4-9530-b2b55d688e91
dc.identifier.otherORCID: /0000-0001-9519-938X/work/55643804
dc.identifier.otherScopus: 85063988925
dc.identifier.otherWOS: 000466986100005
dc.description.abstractA simple graph G = (V, E) is word-representable if there exists a word w over the alphabet V such that letters x and y alternate in w iff xy ∈ E. Word-representable graphs generalize several important classes of graphs. A graph is word-representable if it admits a semi-transitive orientation. We use semi-transitive orientations to enumerate connected non-word-representable graphs up to the size of 11 vertices, which led to a correction of a published result. Obtaining the enumeration results took 3 CPU years of computation. Also, a graph is word-representable if it is k-representable for some k, that is, if it can be represented using k copies of each letter. The minimum such k for a given graph is called graph's representation number. Our computational results in this paper not only include distribution of k-representable graphs on at most 9 vertices, but also have relevance to a known conjecture on these graphs. In particular, we find a new graph on 9 vertices with high representation number. Also, we prove that a certain graph has highest representation number among all comparability graphs on odd number of vertices. Finally, we introduce the notion of a k-semi-transitive orientation refining the notion of a semi-transitive orientation, and show computationally that the refinement is not equivalent to the original definition, unlike the equivalence of k-representability and word-representability.
dc.relation.ispartofJournal of Integer Sequencesen
dc.rights© 2019, the Author(s). This work has been made available online in accordance with the publisher's policies. This is the final published version of the work, which was originally published at
dc.subjectWord-representable graphen
dc.subjectRepresentation numberen
dc.subjectSemi-transitive orientationen
dc.subjectk-semi-transitive orientationen
dc.subjectQA75 Electronic computers. Computer scienceen
dc.titleSolving computational problems in the theory of word-representable graphsen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. School of Computer Scienceen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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