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- W2950971807 abstract "A topological graph is emph{$k$-quasi-planar} if it does not contain $k$ pairwise crossing edges. A topological graph is emph{simple} if every pair of its edges intersect at most once (either at a vertex or at their intersection). In 1996, Pach, Shahrokhi, and Szegedy cite{pach} showed that every $n$-vertex simple $k$-quasi-planar graph contains at most $O(n(log n)^{2k-4})$ edges. This upper bound was recently improved (for large $k$) by Fox and Pach cite{fox} to $n(log n)^{O(log k)}$. In this note, we show that all such graphs contain at most $(nlog^2n)2^{alpha^{c_k}(n)}$ edges, where $alpha(n)$ denotes the inverse Ackermann function and $c_k$ is a constant that depends only on $k$." @default.
- W2950971807 created "2019-06-27" @default.
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- W2950971807 date "2011-06-06" @default.
- W2950971807 modified "2023-10-01" @default.
- W2950971807 title "$k$-quasi planar graphs" @default.
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