TY  - BOOK
AU  - Liu,Yanpei
TI  - Topological theory of graphs
SN  - 9783110476699 (hardcover)
U1  - 511.5 23
PY  - 2017///
CY  - Berlin ; Boston : 
PB  - De Gruyter, 
KW  - Topological graph theory
N1  - 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
N2  - 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
ER  -