PLANARITY IN LINEAR TIME Class notes
نویسنده
چکیده
I give a self-contained exposition of a linear-time planarity algorithm of Shih and Hsu.
منابع مشابه
Circle planarity of level graphs
In this thesis we generalise the notion of level planar graphs in two directions: track planarity and radial planarity. Our main results are linear time algorithms both for the planarity test and for the computation of an embedding, and thus a drawing. Our algorithms use and generalise PQ-trees, which are a data structure for efficient planarity tests. A graph is a level graph, if it has a part...
متن کاملA Planarity Test via Construction Sequences
Linear-time algorithms for testing the planarity of a graph are well known for over 35 years. However, these algorithms are quite involved and recent publications still try to give simpler linear-time tests. We give a conceptually simple reduction from planarity testing to the problem of computing a certain construction of a 3-connected graph. This implies a linear-time planarity test. Our appr...
متن کاملThe thickness of a minor-excluded class of graphs
The thickness problem on graphs is NP-hard and only few results concerning this graph invariant are known. Using a decomposition theorem of Truemper, we show that the thickness of the class of graphs without G 12-minors is less than or equal to two (and therefore, the same is true for the more well-known class of the graphs without K 5-minors). Consequently, the thickness of this class of graph...
متن کاملTwo-page Book Embedding and Clustered Graph Planarity
A 2-page book embedding of a graph places the vertices linearly on a spine (a line segment) and the edges on two pages (two half planes sharing the spine) so that each edge is embedded in one of the pages without edge crossings. Testing whether a given graph admits a 2-page book embedding is known to be NP-complete. In this paper, we study the problem of testing whether a given graph admits a 2...
متن کاملThe Thickness of Graphs withoutK 5 -
The thickness problem on graphs is NP-hard and only few results concerning this graph invariant are known. Using decomposition theorems of Wagner and Truemper, we show that the thickness of graphs without K 5-minors is less than or equal to two. Therefore, the thickness of this class of graphs can be determined with a planarity testing algorithm in linear time.
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تاریخ انتشار 1997