The k-planar crossing number of random graphs and random regular graphs

The k-planar crossing number of random graphs and random regular graphs

We give an explicit extension of Spencer's result on the biplanar crossing number of the Erdos-Renyi random graph $G(n,p)$. In particular, we show that the k-planar crossing number of $G(n,p)$ is almost surely $\Omega((n^2p)^2)$. Along the same lines, we prove that for any fixed $k$, the $k$-pl...

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Hauptverfasser: Asplund, John, Do, Thao, Hamm, Arran, Szekely, Laszlo, Taylor, Libby, Wang, Zhiyu
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Combinatorics
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Zusammenfassung:We give an explicit extension of Spencer's result on the biplanar crossing number of the Erdos-Renyi random graph $G(n,p)$. In particular, we show that the k-planar crossing number of $G(n,p)$ is almost surely $\Omega((n^2p)^2)$. 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 $\Omega ((dn)^2)$ for $d > c_0$ for some constant $c_0=c_0(k)$.
DOI:10.48550/arxiv.1709.08136