{ "item_title" : "Topological Theory of Graphs", "item_author" : [" Yanpei Liu", "University of Science &. Technology "], "item_description" : "This 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.ContentsPreliminaries Polyhedra SurfacesHomology on PolyhedraPolyhedra on the SphereAutomorphisms of a PolyhedronGauss Crossing SequencesCohomology on GraphsEmbeddability on SurfacesEmbeddings on SphereOrthogonality on SurfacesNet EmbeddingsExtremality on SurfacesMatroidal GraphicnessKnot Polynomials", "item_img_path" : "https://covers4.booksamillion.com/covers/bam/3/11/047/669/311047669X_b.jpg", "price_data" : { "retail_price" : "210.00", "online_price" : "210.00", "our_price" : "210.00", "club_price" : "210.00", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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