Automatic graph drawing and readability of diagrams
IEEE Transactions on Systems, Man and Cybernetics
On the thickness of graphs of given degree
Information Sciences: an International Journal
Embedding Graphs into a Three Page Book with O(m log n) Crossings of Edges over the Spine
SIAM Journal on Discrete Mathematics
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
Constrained Point-Set Embeddability of Planar Graphs
Graph Drawing
Planar straight-line point-set embedding of trees with partial embeddings
Information Processing Letters
Upward geometric graph embeddings into point sets
GD'10 Proceedings of the 18th international conference on Graph drawing
On graphs supported by line sets
GD'10 Proceedings of the 18th international conference on Graph drawing
Universal pointsets for 2-coloured trees
GD'10 Proceedings of the 18th international conference on Graph drawing
The hamiltonian augmentation problem and its applications to graph drawing
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Orthogeodesic point-set embedding of trees
GD'11 Proceedings of the 19th international conference on Graph Drawing
Upward point set embeddability for convex point sets is in P
GD'11 Proceedings of the 19th international conference on Graph Drawing
The point-set embeddability problem for plane graphs
Proceedings of the twenty-eighth annual symposium on Computational geometry
Drawing planar graphs on points inside a polygon
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Point-Set embeddability of 2-colored trees
GD'12 Proceedings of the 20th international conference on Graph Drawing
On upward point set embeddability
Computational Geometry: Theory and Applications
| Hi-index | 5.23 |
Let G be a planar graph with n vertices and with a partition of the vertex set into subsets V"0,...,V"k"-"1 for some positive integer 1@?k@?n. Let S be a set of n distinct points in the plane with a partition into subsets S"0,...,S"k"-"1 with |V"i|=|S"i| (0@?i@?k-1). This paper studies the problem of computing a planar polyline drawing of G, such that each vertex of V"i is mapped to a distinct point of S"i. Lower and upper bounds on the number of bends per edge are proved for any 2@?k@?n. In the special case k=n, we improve the upper and lower bounds presented in a paper by Pach and Wenger [J. Pach, R. Wenger, Embedding planar graphs at fixed vertex locations, Graphs and Combinatorics 17 (2001) 717-728]. The upper bound is based on an algorithm for computing a topological book embedding of a planar graph, such that the vertices follow a given left-to-right order and the number of crossings between every edge and the spine is asymptotically optimal, which can be regarded as a result of independent interest.