  A track layout of a graph consists of a vertex coloring and a total order of
each color class, such that no two edges cross between any two color classes.
The track number of a graph is the minimum number of colors required by a track
layout of the graph.
  This paper improves lower and upper bounds on the track number of several
families of planar graphs. We prove that every planar graph has track number at
most $225$ and every planar $3$-tree has track number at most $25$. Then we
show that there exist outerplanar graphs whose track number is $5$, which leads
to the best known lower bound of $8$ for planar graphs. Finally, we investigate
leveled planar graphs and tighten bounds on the track number of weakly leveled
graphs, Halin graphs, and X-trees.
