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Article citations


V. Chvátal, “A Combinatorial Theorem in Plane Geometry,” Journal of Combinatorial Theory, Series B, Vol. 18, No. 1, 1975, pp. 39-41. doi:10.1016/0095-8956(75)90061-1

has been cited by the following article:

  • TITLE: Guarding a Koch Fractal Art Gallery

    AUTHORS: Lauren Cassell, William Roger Fuller

    KEYWORDS: Art Gallery Theorem, Koch Fractal, Difference Equation

    JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.2 No.4, November 1, 2012

    ABSTRACT: This article presents a generalization of the standard art gallery problem to the case where the sides of the gallery are continuous curves which are limits of polygonal arcs. The allowable limiting processes for such generalized art galleries are defined. We construct an art gallery in which one side is the Koch fractal and the other sides are three sides of a rectangle. The appropriate measure of coverage by guards is not the total number of guards but, rather, the guards-to-side ratio. We compute this ratio for the cases of shallow and deep versions of the Koch fractal art gallery.