Topological theory of graphs / Yanpei Liu.
Material type:
- 9783110476699 (hardcover)
- 511.5 23 L783
Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
---|---|---|---|---|---|---|---|
Books | ISI Library, Kolkata | 511.5 L783 (Browse shelf(Opens below)) | Available | 138103 |
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511.5 L657 Graphical methods in research | 511.5 L747 Topics on steiner systems | 511.5 L783 Embeddability in graphs | 511.5 L783 Topological theory of graphs / | 511.5 L896 Matching theory | 511.5 L896 Algebraic methods in graph theory | 511.5 L896 Algebraic methods in graph theory |
Includes bibliographical references and indexes.
1. Premliminaries --
2. Polyhedra --
3. Surfaces --
4. Homology on polyhedra --
5. Polyhedra on the sphere --
6. Automorphism of a polyhedron --
7. Gauss crossing sequences --
8. Cohomology on graphs --
9. Embeddability on surface --
10. Embeddings on sphere --
11. Orthogonality on surfaces --
12. Net embeddings --
13. Extremality on surfaces --
14. Matoidal graphicness --
15. Knot polynomials.
This book presents a topological approach to combinatorial configuration, in particular graphs, by introducing a new pair of homology and cohomology via polyhedral. On this basis, a number of problems are solved using a new approach, such as the embeddability of a graph on a surface (orientable and nonorientable) with given genus, the Gauss crossing conjecture, the graphicness and cographicness of a matroid and so forth. Notably, the specific case of embeddability on a surface of genus zero leads to a number of corollaries, including the theorems of Lefschetz (on double coverings), of MacLane (on cycle bases), and of Whitney (on duality) for planarity. Relevant problems includes the Jordan of axiom in polyhedral forms, efficient methods for extremality for recognizing a variety of embeddings (including rectilinear layouts in VLSI), and pan-polynomials, including those of Jones, Kauffman (on knots), and Tutte (on graphs), among others.
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