Automatic graph drawing and readability of diagrams
IEEE Transactions on Systems, Man and Cybernetics
Simple alternating path problem
Discrete Mathematics
On the thickness of graphs of given degree
Information Sciences: an International Journal
Bipartite embedding of trees in the plane
Discrete Applied Mathematics
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
Network Analysis: Methodological Foundations (Lecture Notes in Computer Science)
Network Analysis: Methodological Foundations (Lecture Notes in Computer Science)
Curve-constrained drawings of planar graphs
Computational Geometry: Theory and Applications
k-colored point-set embeddability of outerplanar graphs
GD'06 Proceedings of the 14th international conference on Graph drawing
Embeddability Problems for Upward Planar Digraphs
Graph Drawing
Point-set embeddings of trees with given partial drawings
Computational Geometry: Theory and Applications
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
Improved algorithms for the point-set embeddability problem for plane 3-trees
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
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Let G be a planar graph with n vertices whose vertex set is partitioned into subsets V0, . . ., Vk-1 for a positive integer 1 ≤ k ≤ n and let S be a set of n distinct points in the plane partitioned into subsets S0, . . ., Sk-1 with |Vi| = |Si| (0 ≤ i ≤ k - 1). This paper studies the problem of computing a crossing-free drawing of G such that each vertex of Vi is mapped to a distinct point of Si. Lower and upper bounds on the number of bends per edge are proved for any 3 ≤ k ≤ n. As a special case, we improve the upper and lower bounds presented in a paper by Pach and Wenger for k = n [Graphs and Combinatorics (2001), 17:717-728].