Stack-number is not bounded by queue-number

@article{Dujmovic2022StacknumberIN,
  title={Stack-number is not bounded by queue-number},
  author={Vida Dujmovi'c and David Eppstein and Robert Hickingbotham and Pat Morin and David R. Wood},
  journal={Comb.},
  year={2022},
  volume={42},
  pages={151-164}
}
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). 
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5 Citations
Background Citations
5
Results Citations
1

5 Citations

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References

SHOWING 1-10 OF 60 REFERENCES
Bounded-Degree Graphs have Arbitrarily Large Queue-Number
  • D. Wood
  • Mathematics
    Discret. Math. Theor. Comput. Sci.
  • 2008
It is proved that there exist graphs of bounded degree with arbitrarily large queue-number. In particular, for all Δ ≥ 3 and for all sufficiently large n , there is a simple Δ -regular n -vertex…
Queue Layouts of Graph Products and Powers
  • D. Wood
  • Mathematics
    Discret. Math. Theor. Comput. Sci.
  • 2005
TLDR
This paper studies queue layouts of graph products and powers by partitioning E(G) into k sets, each of which contains no two edges that are nested in σ.
On 3-pushdown graphs with large separators
TLDR
It is shown that for every fixeds and all alln large enough, there is ann-vertex 3-pushdown graph whose smallest separator contains at leastΩ(n/ls(n) vertices.
Embedding planar graphs in four pages
Planar Graphs have Bounded Queue-Number
Graph product structure for non-minor-closed classes
TLDR
It is proved that every planar graph is a subgraph of the strong product of a graph of bounded treewidth and a path and implies, amongst other results, that $k$-planar graphs have non-repetitive chromatic number upper-bounded by a function of $k$.
Planar graphs of bounded degree have bounded queue number
TLDR
It is proved that planar graphs of bounded degree (which may have unbounded treewidth) have bounded queue number, which means that every planar graph of boundeddegree admits a three-dimensional straight-line grid drawing in linear volume.
Expansion in SL 2$${(\mathbb{R})}$$ and monotone expanders
This work presents an explicit construction of a family of monotone expanders, which are bi-partite expander graphs whose edge-set is defined by (partial) monotone functions. The family is (roughly)…
Layouts of Expander Graphs
TLDR
3-monotone bipartite expanders are constructed, which is best possible, and it is shown that the same graphs admit 3-page book embeddings, 2-queue layouts, 4-track layouts, and have simple thickness 2.
Planar Graphs that Need Four Pages
...
...