Please use this identifier to cite or link to this item: https://idr.l1.nitk.ac.in/jspui/handle/123456789/12910
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dc.contributor.authorAlon, N.
dc.contributor.authorBasavaraju, M.
dc.contributor.authorChandran, L.S.
dc.contributor.authorMathew, R.
dc.contributor.authorRajendraprasad, D.
dc.date.accessioned2020-03-31T08:42:24Z-
dc.date.available2020-03-31T08:42:24Z-
dc.date.issued2018
dc.identifier.citationJournal of Graph Theory, 2018, Vol.89, 1, pp.14-25en_US
dc.identifier.urihttp://idr.nitk.ac.in/jspui/handle/123456789/12910-
dc.description.abstractThe separation dimension 𝜋?(G) of a hypergraph G is the smallest natural number k for which the vertices of G can be embedded in Rk so that any pair of disjoint edges in G can be separated by a hyperplane normal to one of the axes. Equivalently, it is the cardinality of a smallest family F of total orders of V(G), such that for any two disjoint edges of G, there exists at least one total order in F in which all the vertices in one edge precede those in the other. Separation dimension is a monotone parameter; adding more edges cannot reduce the separation dimension of a hypergraph. In this article, we discuss the influence of separation dimension and edge-density of a graph on one another. On one hand, we show that the maximum separation dimension of a k-degenerate graph on n vertices is O(k lg lg n) and that there exists a family of 2-degenerate graphs with separation dimension ?(lg lg n). On the other hand, we show that graphs with bounded separation dimension cannot be very dense. Quantitatively, we prove that n-vertex graphs with separation dimension s have at most 3(4 lg n)s?2 edges. We do not believe that this bound is optimal and give a question and a remark on the optimal bound. 2018 Wiley Periodicals, Inc.en_US
dc.titleSeparation dimension and sparsityen_US
dc.typeArticleen_US
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