{"product_id":"combinatorial-nullstellensatz-xuding-zhu-9780367686949","title":"Combinatorial Nullstellensatz: With Applications to Graph Colouring","description":"\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\n\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 \u003cp\u003e \u003c\/p\u003e\n\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 \u003cp\u003e \u003c\/p\u003e\n\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 \u003cp\u003e\u003c\/p\u003e\n\u003c\/ol\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eIt is suited as a reference book for a graduate course in mathematics.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Xuding Zhu, R. Balakrishnan\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0367686945\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780367686949\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e CRC Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 06\/01\/2021\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 134\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.71lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 8.50h x 5.50w x 0.38d\u003c\/p\u003e","brand":"Xuding Zhu","offers":[{"title":"Hardcover","offer_id":44450282340607,"sku":"9780367686949","price":69.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_098b9a03-ba5b-46c0-b79a-b53abf8e57f7.jpg?v=1698503905","url":"https:\/\/www.whiterainbookhouse.com\/products\/combinatorial-nullstellensatz-xuding-zhu-9780367686949","provider":"WR Book House","version":"1.0","type":"link"}