On the bend-number of planar and outerplanar graphs
Daniel Heldt, Kolja Knauer, Torsten Ueckerdt
TL;DR
This paper investigates the bend-number of planar and outerplanar graphs, confirming the maximum for outerplanar graphs is 2 and improving bounds for planar graphs to between 3 and 4.
Contribution
It proves the maximum bend-number for outerplanar graphs is 2 and refines the bounds for planar graphs' bend-number from 2-5 to 3-4.
Findings
Maximum bend-number of outerplanar graphs is 2.
Maximum bend-number of planar graphs is between 3 and 4.
Abstract
The bend-number b(G) of a graph G is the minimum k such that G may be represented as the edge intersection graph of a set of grid paths with at most k bends. We confirm a conjecture of Biedl and Stern showing that the maximum bend-number of outerplanar graphs is 2. Moreover we improve the formerly known lower and upper bound for the maximum bend-number of planar graphs from 2 and 5 to 3 and 4, respectively.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Graph Theory Research · Interconnection Networks and Systems