4 research outputs found
Notes on Graph Product Structure Theory
It was recently proved that every planar graph is a subgraph of the strong
product of a path and a graph with bounded treewidth. This paper surveys
generalisations of this result for graphs on surfaces, minor-closed classes,
various non-minor-closed classes, and graph classes with polynomial growth. We
then explore how graph product structure might be applicable to more broadly
defined graph classes. In particular, we characterise when a graph class
defined by a cartesian or strong product has bounded or polynomial expansion.
We then explore graph product structure theorems for various geometrically
defined graph classes, and present several open problems.Comment: 19 pages, 0 figure
Stack-number is not bounded by queue-number
We describe a family of graphs with queue-number at most 4 but unbounded
stack-number. This resolves open problems of Heath, Leighton and Rosenberg
(1992) and Blankenship and Oporowski (1999)