On the thickness of graphs of given degree
Information Sciences: an International Journal
Straight line embeddings of rooted star forests in the plane
Discrete Applied Mathematics
On embedding an outer-planar graph in a point set
Computational Geometry: Theory and Applications
Curve-constrained drawings of planar graphs
Computational Geometry: Theory and Applications
Drawing colored graphs on colored points
Theoretical Computer Science
Point-set embedding of trees with edge constraints
GD'07 Proceedings of the 15th international conference on Graph drawing
Drawing colored graphs with constrained vertex positions and few bends per edge
GD'07 Proceedings of the 15th international conference on Graph drawing
Drawing planar graphs on points inside a polygon
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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This paper starts the investigation of a constrained version of the point-set embeddability problem. Let G = (V,E) be a planar graph with n vertices, G′ = (V′,E′) a subgraph of G, and S a set of n distinct points in the plane. We study the problem of computing a point-set embedding of G on S subject to the constraint that G′ is drawn with straight-line edges. Different drawing algorithms are presented that guarantee small curve complexity of the resulting drawing, i.e. a small number of bends per edge. It is proved that: (i) If G′ is an outerplanar graph and S is any set of points in convex position, a point-set embedding of G on S can be computed such that the edges of E ∖ E′ have at most 4 bends each. (ii) If S is any set of points in general position and G′ is a face of G or if it is a simple path, the curve complexity of the edges of E ∖ E′ is at most 8. (iii) If S is in general position and G′ is a set of k disjoint paths, the curve complexity of the edges of E ∖ E′ is O(2 k ).