Open AccessPlanar embeddability of the vertices of a graph using a fixed point set is NP-hard
Author(s) -
Sergio Cabello
Publication year - 2006
Publication title -
journal of graph algorithms and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.387
H-Index - 38
ISSN - 1526-1719
DOI - 10.7155/jgaa.00132
Subject(s) - combinatorics , mathematics , planar , planar graph , graph , set (abstract data type) , discrete mathematics , computer science , computer graphics (images) , programming language
Let G = (V, E) be a graph with n vertices and let P be a set of n points in the plane. We show that deciding whether there is a planar straight-line embedding of G such that the vertices V are embedded onto the points P is NP-complete, even when G is 2-connected and 2-outerplanar. This settles an open problem posed in [2, 4, 13].
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