The maximum number of tangencies among convex regions with a triangle-free intersection graph
نویسنده
چکیده
Let t(C) be the number of tangent pairs among a set C of n Jordan regions in the plane. Pach, Suk, and Treml [6] showed that if C consists of convex bodies and its intersection graph is bipartite then t(C) ≤ 4n−Θ(1), and, moreover, there are such sets that admit at least 3n−Θ( √ n) tangencies. We close this gap and generalize their result by proving that the correct bound is 3n−Θ(1), even when the intersection graph of C is only assumed to be triangle-free.
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تاریخ انتشار 2011