{"product_id":"combinatorial-nullstellensatz-with-applications-to-graph-colouring-9780367686949","title":"Combinatorial Nullstellensatz: With Applications to Graph Colouring","description":"\u003cp\u003e • Author(s): Xuding Zhu\u003cbr\u003e • Publisher: Taylor \u0026amp; Francis\u003cbr\u003e • Publisher Imprint: CRC Press\u003cbr\u003e • BISAC: Algebra - General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eCombinatorial Nullstellensatz is a novel theorem in algebra introduced by Noga Alon to tackle combinatorial problems in diverse areas of mathematics. This book focuses on the applications of this theorem to graph colouring. A key step in the applications of Combinatorial Nullstellensatz is to show that the coefficient of a certain monomial in the expansion of a polynomial is nonzero. The major part of the book concentrates on three methods for calculating the coefficients: \u003c\/p\u003e\u003col\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eAlon-Tarsi orientation: The task is to show that a graph has an orientation with given maximum out-degree and for which the number of even Eulerian sub-digraphs is different from the number of odd Eulerian sub-digraphs. In particular, this method is used to show that a graph whose edge set decomposes into a Hamilton cycle and vertex-disjoint triangles is 3-choosable, and that every planar graph has a matching whose deletion results in a 4-choosable graph.\u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eInterpolation formula for the coefficient: This method is in particular used to show that toroidal grids of even order are 3-choosable, r-edge colourable r-regular planar graphs are r-edge choosable, and complete graphs of order p+1, where p is a prime, are p-edge choosable. \u003c\/li\u003e \u003cp\u003e \u003c\/p\u003e \u003cli\u003eCoefficients as the permanents of matrices: This method is in particular used in the study of the list version of vertex-edge weighting and to show that every graph is (2,3)-choosable.\u003c\/li\u003e \u003c\/ol\u003e\u003cp\u003eIt is suited as a reference book for a graduate course in mathematics.\u003c\/p\u003e","brand":"Taylor \u0026 Francis","offers":[{"title":"Hardcover","offer_id":45241122390167,"sku":"9780367686949","price":5752.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780367686949.webp?v=1767916342","url":"https:\/\/atlanticbooks.com\/products\/combinatorial-nullstellensatz-with-applications-to-graph-colouring-9780367686949","provider":"Atlantic Books","version":"1.0","type":"link"}