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On the connectedness and diameter of a geometric Johnson graph

Abstract : Let P be a set of n points in general position in the plane. A subset I of P is called an island if there exists a convex set C such that I = P \C. In this paper we define the generalized island Johnson graph of P as the graph whose vertex consists of all islands of P of cardinality k, two of which are adjacent if their intersection consists of exactly l elements. We show that for large enough values of n, this graph is connected, and give upper and lower bounds on its diameter.
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Crevel Bautista-Santiago, Javier Cano, Ruy Fabila-Monroy, David Flores-Peñaloza, Hernàn González-Aguilar, et al.. On the connectedness and diameter of a geometric Johnson graph. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2013, Vol. 15 no. 3 (3), pp.21--30. ⟨hal-00966378⟩

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