On the Queue Number of Planar Graphs
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We prove that planar graphs have $O(\log^2 n)$ queue number, thus improving upon the previous $O(\sqrt n)$ upper bound. Consequently, planar graphs admit three-dimensional straight-line crossing-free grid drawings in $O(n \log^8 n)$ volume, thus improving upon the previous $O(n^{3/2})$ upper bound.