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Planar Graphs: Four Color Theorem, Planar Graph, Tait's Conjecture, Planar Separator Theorem, Apex Graph, Circle Packing Theorem(English)

Planar Graphs: Four Color Theorem, Planar Graph, Tait's Conjecture, Planar Separator Theorem, Apex Graph, Circle Packing Theorem(English)

          
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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 38. Chapters: Four color theorem, Planar graph, Tait's conjecture, Planar separator theorem, Apex graph, Circle packing theorem, Outerplanar graph, Steinitz's theorem, FKT algorithm, Fary's theorem, Planarity testing, Barnette's conjecture, Series-parallel graph, Scheinerman's conjecture, Cactus graph, Herschel graph, Goldner-Harary graph, Halin graph, Durer graph, Grotzsch's theorem, Dual graph, Squaregraph, Wheel graph, Friendship graph, Polyhedral graph, Bull graph, Frucht graph, Butterfly graph, Book, Schnyder's theorem, Bidiakis cube, Fraysseix-Rosenstiehl's planarity criterion, Ladder graph, Lattice graph, Grinberg's theorem, Mac Lane's planarity criterion. Excerpt: In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split into smaller pieces by removing a small number of vertices. Specifically, the removal of O( n) vertices from an n-vertex graph (where the O invokes big O notation) can partition the graph into disjoint subgraphs each of which has at most 2n/3 vertices. A weaker form of the separator theorem with O( n log n) vertices in the separator instead of O( n) was originally proven by Ungar (1951), and the form with the tight asymptotic bound on the separator size was first proven by Lipton & Tarjan (1979). Since their work, the separator theorem has been reproven in several different ways, the constant in the O( n) term of the theorem has been improved, and it has been extended to certain classes of nonplanar graphs. Repeated application of the separator theorem produces a separator hierarchy which may take the form of either a tree decomposition or a branch-decomposition of the graph. Separator hierarchies may be used to devise efficient divide and conquer algorithms for planar graphs, and dynamic programming on these hiera...


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Product Details
  • ISBN-13: 9781233107636
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 40
  • Series Title: English
  • Sub Title: Four Color Theorem, Planar Graph, Tait's Conjecture, Planar Separator Theorem, Apex Graph, Circle Packing Theorem
  • Width: 189 mm
  • ISBN-10: 1233107631
  • Publisher Date: 19 Aug 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Spine Width: 2 mm
  • Weight: 91 gr


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