A Linear Upper Bound on the Rectilinear Crossing Number
نویسنده
چکیده
It is proved that the rectilinear crossing number of every graph with bounded tree-width and bounded degree is linear in the num-
منابع مشابه
New Lower Bounds for the Number of (<=k)-Edges and the Rectilinear Crossing Number of Kn
We provide a new lower bound on the number of (≤ k)-edges of a set of n points in the plane in general position. We show that for 0 ≤ k ≤ bn−2 2 c the number of (≤ k)-edges is at least Ek(S) ≥ 3 ( k + 2 2 ) + k ∑ j=b3 c (3j − n + 3), which, for b3 c ≤ k ≤ 0.4864n, improves the previous best lower bound in [11]. As a main consequence, we obtain a new lower bound on the rectilinear crossing numbe...
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تاریخ انتشار 2005