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dc.contributor.authorDiego Gutiérrez, Victor
dc.contributor.authorSerra Albó, Oriol
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationDiego , V., Serra, O. On a problem by Shapozenko on Johnson Graphs. "Graphs and combinatorics", Setembre 2018, vol. 34, núm. 5, p. 947-964.
dc.descriptionThe final publication is available at Springer via
dc.description.abstractThe Johnson graph J(n, m) has the m-subsets of {1,2,…,n} as vertices and two subsets are adjacent in the graph if they share m-1 elements. Shapozenko asked about the isoperimetric function µn,m(k) of Johnson graphs, that is, the cardinality of the smallest boundary of sets with k vertices in J(n, m) for each 1=k=(nm) . We give an upper bound for µn,m(k) and show that, for each given k such that the solution to the Shadow Minimization Problem in the Boolean lattice is unique, and each sufficiently large n, the given upper bound is tight. We also show that the bound is tight for the small values of k=m+1 and for all values of k when m=2 .
dc.format.extent18 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
dc.subject.lcshGraph theory
dc.subject.otherJohnson graph
dc.subject.otherIsoperimetric problem
dc.subject.otherShift compression
dc.titleOn a problem by Shapozenko on Johnson Graphs
dc.subject.lemacGrafs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::05 Combinatorics::05C Graph theory
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
upcommons.citation.authorDiego, V.; Serra, O.
upcommons.citation.publicationNameGraphs and combinatorics

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