
On Families of Planar DAGs with Constant Stack Number
A kstack layout (or kpage book embedding) of a graph consists of a tot...
read it

Simultaneous Embedding of Colored Graphs
A set of colored graphs are compatible, if for every color i, the number...
read it

Dynamic list coloring of 1planar graphs
A graph is kplanar if it can be drawn in the plane so that each edge is...
read it

Planar Ramsey graphs
We say that a graph H is planar unavoidable if there is a planar graph G...
read it

SMS in PACE 2020
We describe SMS, our submission to the exact treedepth track of PACE 202...
read it

Train Tracks with Gaps: Applying the Probabilistic Method to Trains
We identify a tradeoff curve between the number of wheels on a train car...
read it

Coloring outerplanar graphs and planar 3trees with small monochromatic components
In this work, we continue the study of vertex colorings of graphs, in wh...
read it
Improved Bounds for Track Numbers of Planar Graphs
A track layout of a graph consists of a vertex coloring and of a total order of each color class, such that the edges between each pair of colors form a noncrossing set. 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 3tree has track number at most 25. Then we show that there exist outerplanar graphs whose track number is 5, which leads 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 Xtrees.
READ FULL TEXT
Comments
There are no comments yet.