332 research outputs found
Stack and Queue Layouts via Layered Separators
It is known that every proper minor-closed class of graphs has bounded
stack-number (a.k.a. book thickness and page number). While this includes
notable graph families such as planar graphs and graphs of bounded genus, many
other graph families are not closed under taking minors. For fixed and ,
we show that every -vertex graph that can be embedded on a surface of genus
with at most crossings per edge has stack-number ;
this includes -planar graphs. The previously best known bound for the
stack-number of these families was , except in the case
of -planar graphs. Analogous results are proved for map graphs that can be
embedded on a surface of fixed genus. None of these families is closed under
taking minors. The main ingredient in the proof of these results is a
construction proving that -vertex graphs that admit constant layered
separators have stack-number.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
Mixed Linear Layouts of Planar Graphs
A -stack (respectively, -queue) layout of a graph consists of a total
order of the vertices, and a partition of the edges into sets of
non-crossing (non-nested) edges with respect to the vertex ordering. In 1992,
Heath and Rosenberg conjectured that every planar graph admits a mixed
-stack -queue layout in which every edge is assigned to a stack or to a
queue that use a common vertex ordering.
We disprove this conjecture by providing a planar graph that does not have
such a mixed layout. In addition, we study mixed layouts of graph subdivisions,
and show that every planar graph has a mixed subdivision with one division
vertex per edge.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
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