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Embeddability in Graphs

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04 December 2010
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This monograph provides a theoretical treatment of the problems related to the embeddability of graphs. Among these problems are the planarity and planar embeddings of a graph, the Gaussian crossing problem, the isomorphisms of polyhedra, surface embeddability, problems concerning graphic and cographic matroids and the knot problem from topology to combinatorics are discussed. Rectilinear embeddability, and the net-embeddability of a graph, which appears from the VSLI circuit design and has been much improved by the author recently, is also illustrated. Furthermore, some optimization problems related to planar and rectilinear embeddings of graphs, including those of finding the shortest convex embedding with a boundary condition and the shortest triangulation for given points on the plane, the bend and the area minimizations of rectilinear embeddings, and several kinds of graph decompositions are specially described for conditions efficiently solvable.
At the end of each chapter, the Notes Section sets out the progress of related problems, the background in theory and practice, and some historical remarks. Some open problems with suggestions for their solutions are mentioned for further research.

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    Product Details
    ISBN-13
    9789048145997
    Author
    Liu Yanpei
    Publisher
    Springer Nature B.V.
    Published
    04 December 2010
    Format
    Paperback / softback

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    RRP: $228.69
    $225.26
    Ships in 3-5 business days

    Delivery estimate

    Hurry up! Current stock:

    Embeddability in Graphs

    RRP: $228.69
    $225.26

    Description

    This monograph provides a theoretical treatment of the problems related to the embeddability of graphs. Among these problems are the planarity and planar embeddings of a graph, the Gaussian crossing problem, the isomorphisms of polyhedra, surface embeddability, problems concerning graphic and cographic matroids and the knot problem from topology to combinatorics are discussed. Rectilinear embeddability, and the net-embeddability of a graph, which appears from the VSLI circuit design and has been much improved by the author recently, is also illustrated. Furthermore, some optimization problems related to planar and rectilinear embeddings of graphs, including those of finding the shortest convex embedding with a boundary condition and the shortest triangulation for given points on the plane, the bend and the area minimizations of rectilinear embeddings, and several kinds of graph decompositions are specially described for conditions efficiently solvable.
    At the end of each chapter, the Notes Section sets out the progress of related problems, the background in theory and practice, and some historical remarks. Some open problems with suggestions for their solutions are mentioned for further research.

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