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• W2898887851 abstract "A emph{queue layout} of a graph consists of a emph{linear order} of its vertices and a partition of its edges into emph{queues}, so that no two independent edges of the same queue are nested. The emph{queue number} of a graph is the minimum number of queues required by any of its queue layouts. A long-standing conjecture by Heath, Leighton and Rosenberg states that the queue number of planar graphs is bounded. This conjecture has been partially settled in the positive for several subfamilies of planar graphs (most of which have bounded treewidth). In this paper, we make a further important step towards settling this conjecture. We prove that planar graphs of bounded degree (which may have unbounded treewidth) have bounded queue number. A notable implication of this result is that every planar graph of bounded degree admits a three-dimensional straight-line grid drawing in linear volume. Further implications are that every planar graph of bounded degree has bounded track number, and that every $k$-planar graph (i.e., every graph that can be drawn in the plane with at most $k$ crossings per edge) of bounded degree has bounded queue number." @default.
• W2898887851 created "2018-11-09" @default.
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• W2898887851 date "2018-11-02" @default.
• W2898887851 modified "2023-09-27" @default.
• W2898887851 title "Planar Graphs of Bounded Degree have Constant Queue Number." @default.
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