Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
A linear time algorithm for finding tree-decompositions of small treewidth
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Efficient and constructive algorithms for the pathwidth and treewidth of graphs
Journal of Algorithms
On Linear Recognition of Tree-Width at Most Four
SIAM Journal on Discrete Mathematics
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Dynamic Programming on Graphs with Bounded Treewidth
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Computational Geometry: Theory and Applications
Straight line embeddings of cubic planar graphs with integer edge lengths
Journal of Graph Theory
Area-universal rectangular layouts
Proceedings of the twenty-fifth annual symposium on Computational geometry
Subclasses of k-trees: Characterization and recognition
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
Treewidth: structure and algorithms
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Point-set embeddings of plane 3-trees
GD'10 Proceedings of the 18th international conference on Graph drawing
The planar slope number of planar partial 3-trees of bounded degree
GD'09 Proceedings of the 17th international conference on Graph Drawing
Drawing planar 3-trees with given face-areas
GD'09 Proceedings of the 17th international conference on Graph Drawing
Computing cartograms with optimal complexity
Proceedings of the twenty-eighth annual symposium on Computational geometry
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We study straight-line drawings of planar graphs such that each interior face has a prescribed area. It was known that such drawings exist for all planar graphs with maximum degree 3. We show here that such drawings exist for all planar partial 3-trees, i.e., subgraphs of a triangulated planar graph obtained by repeatedly inserting a vertex in one triangle and connecting it to all vertices of the triangle. Moreover, vertices have rational coordinates if the face areas are rational, and we can bound the resolution. We also give some negative results for other graph classes.