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A \emph{$k$-track} layout of a graph consists of a vertex $k$ colouring, anda total order of each vertex colour class, such that between each pair ofcolour classes no two edges cross. A \emph{$k$-queue} layout of a graphconsists of a total order of the vertices, and a partition of the edges into$k$ sets such that no two edges that are in the same set are nested withrespect to the vertex ordering. The \emph{track number} (\emph{queue number})of a graph $G$, is the minimum $k$ such that $G$ has a $k$-track ($k$-queue)layout. This paper proves that every $n$-vertex plane graph has constant-boundtrack and queue numbers. The result implies that every plane has a 3Dcrossing-free straight-line grid drawing in $O(n)$ volume. The proof utilizes anovel graph partition technique.

Layouts for Plane Graphs on Constant Number of Tracks