On graph thickness, geometric thickness, and separator theorems
CA Duncan - Computational Geometry, 2011 - Elsevier
Computational Geometry, 2011•Elsevier
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.
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.
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.
Elsevier
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