{"product_id":"topological-theory-of-graphs-von-yanpei-liu","title":"Topological Theory of Graphs","description":"\n                                \n                \u003cp\u003eThis book presents a topological approach to combinatorial configurations, in particular graphs, by introducing a new pair of homology and cohomology via polyhedra. 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 include the Jordan axiom in polyhedral forms, efficient methods for extremality and 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. \u003c\/p\u003e\n                                 \n                \n                \u003cp\u003e\u003c\/p\u003e\n                                 \n                \n                \u003cp\u003e\n                                        \n                    \u003cstrong\u003eContents\u003c\/strong\u003e\n                                         \n                \n                \u003c\/p\u003e\n                                Preliminaries \n                \n                \u003cp\u003e\u003c\/p\u003e\n                                Polyhedra \n                \n                \u003cp\u003e\u003c\/p\u003e\n                                Surfaces \n                \n                \u003cp\u003e\u003c\/p\u003e\n                                 \n                \n                \u003cp\u003eHomology on Polyhedra \u003c\/p\u003e\n                                 \n                \n                \u003cp\u003ePolyhedra on the Sphere \u003c\/p\u003e\n                                 \n                \n                \u003cp\u003eAutomorphisms of a Polyhedron \u003c\/p\u003e\n                                 \n                \n                \u003cp\u003eGauss Crossing Sequences \u003c\/p\u003e\n                                 \n                \n                \u003cp\u003eCohomology on Graphs \u003c\/p\u003e\n                                 \n                \n                \u003cp\u003eEmbeddability on Surfaces \u003c\/p\u003e\n                                 \n                \n                \u003cp\u003eEmbeddings on Sphere \u003c\/p\u003e\n                                 \n                \n                \u003cp\u003eOrthogonality on Surfaces \u003c\/p\u003e\n                                 \n                \n                \u003cp\u003eNet Embeddings \u003c\/p\u003e\n                                 \n                \n                \u003cp\u003eExtremality on Surfaces \u003c\/p\u003e\n                                 \n                \n                \u003cp\u003eMatroidal Graphicness \u003c\/p\u003e\n                                 \n                \n                \u003cp\u003eKnot Polynomials \u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783110476699\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Hardcover - 9783110476699","offer_id":40527061745757,"sku":"9783110476699","price":159.95,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/644a046a-2025-48dd-baf0-e36648c28404.jpg?v=1778043653","url":"https:\/\/shop.autorenwelt.de\/en\/products\/topological-theory-of-graphs-von-yanpei-liu","provider":"Autorenwelt Shop","version":"1.0","type":"link"}