# Separating Geometric Thickness from Book Thickness

@article{Eppstein2001SeparatingGT, title={Separating Geometric Thickness from Book Thickness}, author={David Eppstein}, journal={ArXiv}, year={2001}, volume={math.CO/0109195} }

We show that geometric thickness and book thickness are not asymptotically equivalent: for every t, there exists a graph with geometric thickness two and book thickness >= t.

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## 14 Citations

Separating Thickness from Geometric Thickness

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- 2002

We show that graph-theoretic thickness and geometric thickness are not asymptotically equivalent: for every t, there exists a graph with thickness three and geometric thickness ? t.

The geometric thickness of low degree graphs

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It is proved that the geometric thickness of graphs whose maximum degree is no more than four is two, and an embedding algorithm for graphs with maximum degree three that uses an n x n grid and a more complex algorithm for embedding a graph withmaximum degree four.

Graph Treewidth and Geometric Thickness Parameters

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It is shown that the lower bound for thickness can be matched by an upper bound, even in the more restrictive geometric setting, and that for graphs of treewidth k, the maximum thickness and the maximum geometric thickness both equal ⌈k/2⌉.

Bounded-Degree Graphs have Arbitrarily Large Geometric Thickness

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This work proves that there exists Delta-regular graphs with arbitrarily large geometric thickness, and proves that for all Delta >= 9 and for all large n, there exists a Delta- regular graph with geometric thickness at least c Delta^{1/2} n^{1 /2 - 4/Delta - epsilon}.

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Consider a drawing of a graph G in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of G, is the classical graph parameter…

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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…

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This paper shows that if a partition or covering of the tree by subtrees of bounded degree satisfies some natural properties, then there is a drawing of the entire tree such that each of the given subtrees is drawn as a minimum spanning tree of its vertex set.

Thickness and Antithickness of Graphs

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Questions about duality between crossings and non-crossings in graph drawings via the notions of thickness and antithickness are studied, with an emphasis on extremal questions.

## References

SHOWING 1-6 OF 6 REFERENCES

The Thickness of Graphs: A Survey

- MathematicsGraphs Comb.
- 1998

A state-of-the-art survey of the thickness of a graph from both a theoretical and a practical point of view is given and some modifications of a basic heuristic are investigated for evaluating the thickness and determining a decomposition of agraph in planar subgraphs.

Ramsey Theory

- Physics
- 2020

a temporary collection of stars, we earthlings observe from the edge of an ordinary galaxy. Yet most stargazers agree that the night sky appears to be filled with constellations in the shape of…

Geometric Thickness in a Grid of Linear Area

- Mathematics, Computer ScienceElectron. Notes Discret. Math.
- 2001

Graph Drawing: Algorithms for the Visualization of Graphs

- Prentice Hall
- 1999