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CORR
2008
Springer

Obfuscated Drawings of Planar Graphs

8 years 2 months ago
Obfuscated Drawings of Planar Graphs
Given a planar graph G, we consider drawings of G in the plane where edges are represented by straight line segments (which possibly intersect). Such a drawing is specified by an injective embedding of the vertex set of G into the plane. Let fix(G, ) be the maximum integer k such that there exists a crossing-free redrawing of G which keeps k vertices fixed, i.e., there exist k vertices v1, . . . , vk of G such that (vi) = (vi) for i = 1, . . . , k. We give examples of planar graphs G along with a drawing for which fix(G, ) = O( n). In fact, such a drawing exists even if it is presupposed that the vertices occupy any prescribed set of points on the boundary of a convex body. We also consider the parameter obf (G) of a graph G which is equal to the maximum number of edge crossings over all straight line drawings of G. We give examples of planar graphs with obf (G) ( 9 4 - o(1))n2 and prove that obf (T) ( 13 8 - o(1))n2 for every triangulation T. We also show that a given triangul...
Mihyun Kang, Oleg Pikhurko, Alexander Ravsky, Math
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where CORR
Authors Mihyun Kang, Oleg Pikhurko, Alexander Ravsky, Mathias Schacht, Oleg Verbitsky
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