# 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).

## 5 Citations

Three-dimensional graph products with unbounded stack-number

- MathematicsArXiv
- 2022

We prove that the stack-number of the strong product of three n-vertex paths is Θ(n). The best previously known upper bound wasO(n). No non-trivial lower bound was known. This is the first explicit…

Code generation criteria for buffered exposed datapath architectures from dataflow graphs

- Computer ScienceLCTES
- 2022

Inspired by results on queue layouts in graph drawing, constraints for the node and edge orderings of the dataflow graphs are determined to ensure the first-in-first-out behavior of the buffers.

Shallow Minors, Graph Products and Beyond Planar Graphs

- Mathematics
- 2021

The planar graph product structure theorem of Dujmović, Joret, Micek, Morin, Ueckerdt, and Wood [J. ACM 2020] states that every planar graph is a subgraph of the strong product of a graph with…

Linear Layouts of Complete Graphs

- MathematicsGraph Drawing
- 2021

Upper and lower bounds on these four parameters for the complete graph Kn on n vertices are presented, and in three cases the exact result up to an additive constant is obtained.

## References

SHOWING 1-10 OF 60 REFERENCES

Bounded-Degree Graphs have Arbitrarily Large Queue-Number

- MathematicsDiscret. 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

- MathematicsDiscret. Math. Theor. Comput. Sci.
- 2005

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

- MathematicsComb.
- 1989

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.

Graph product structure for non-minor-closed classes

- Mathematics
- 2019

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

- MathematicsSTOC
- 2019

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

- Mathematics
- 2013

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

- MathematicsChic. J. Theor. Comput. Sci.
- 2016

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.