k-planar Crossing Number of Random Graphs and Random Regular Graphs
نویسندگان
چکیده
We give an explicit extension of Spencer’s result on the biplanar crossing number of the ErdősRényi random graph G(n, p). In particular, we show that the k-planar crossing number of G(n, p) is almost surely Ω((np)). Along the same lines, we prove that for any fixed k, the k-planar crossing number of various models of random d-regular graphs is Ω((dn)) for d > c0 for some constant c0 = c0(k).
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تاریخ انتشار 2017