Efficient algorithms for optimization and selection on series-parallel graphs
SIAM Journal on Algebraic and Discrete Methods
On the thickness of graphs of given degree
Information Sciences: an International Journal
SIAM Journal on Discrete Mathematics
Graphs with E edges have pagenumber E O
Journal of Algorithms
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
The geometric thickness of low degree graphs
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Excluding any graph as a minor allows a low tree-width 2-coloring
Journal of Combinatorial Theory Series B
On simultaneous planar graph embeddings
Computational Geometry: Theory and Applications
Graph Treewidth and Geometric Thickness Parameters
Discrete & Computational Geometry
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We investigate the relationship between geometric thickness, thickness, outerthickness, and arboricity of graphs. In particular, we prove that all graphs with arboricity two or outerthickness two have geometric thickness O(logn). The technique used can be extended to other classes of graphs so long as a separator theorem exists. For example, we can apply it to show the known bound that thickness two graphs have geometric thickness O(n), yielding a simple construction in the process.