Embeddability in graphs
Author(s)
Bibliographic Information
Embeddability in graphs
（Mathematics and its applications, v. 338 . China series）
Science Press , Kluwer Academic Publishers, c1995
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Includes bibliographical references and index
Description and Table of Contents
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.
Table of Contents
Preface. 1. Preliminaries. 2. Trees in Graphs. 3. Spaces in Graphs. 4. Planar Graphs. 5. Planarity. 6. Gauss Crossing Problem. 7. Planar Embeddings. 8. Rectilinear Embeddability. 9. Net Embeddability. 10. Isomorphisms in Polyhedra. 11. Decompositions of Graphs. 12. Surface Embeddability. 13. Extremal Problems. 14. Graphic and Cographic Matroids. 15. Invariants on Knots. References. Index.
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