A k-stack (respectively, k-queue) layout of a graph consists of a total
order of the vertices, and a partition of the edges into k 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
1-stack 1-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
