Xuding Zhu's Books

Combinatorial Nullstellensatz

With Applications to Graph Colouring

By: Xuding Zhu,R. Balakrishnan

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Combinatorial Nullstellensatz

With Applications to Graph Colouring

By: Xuding Zhu,R. Balakrishnan

Combinatorial 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: Alon-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. Interpolation 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. Coefficients 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. It is suited as a reference book for a graduate course in mathematics.

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Page Count

150

Publisher

CRC Press

Published Date

ISBN 10

1000426688

ISBN 13

9781000426687

Combinatorial Nullstellensatz

With Applications to Graph Colouring

By: Xuding Zhu,R. Balakrishnan

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Combinatorial Nullstellensatz

With Applications to Graph Colouring

By: Xuding Zhu,R. Balakrishnan

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Publisher

CRC Press

Published Date

ISBN 10

1000426696

ISBN 13

9781000426694

Combinatorial Optimization and Applications

5th International Conference, COCOA 2011, Zhangjiajie, China, August 4-6, 2011, Proceedings

By: Weifan Wang,Xuding Zhu,Ding-Zhu Du

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Combinatorial Optimization and Applications

5th International Conference, COCOA 2011, Zhangjiajie, China, August 4-6, 2011, Proceedings

By: Weifan Wang,Xuding Zhu,Ding-Zhu Du

This book constitutes the refereed proceedings of the 5th International Conference on Combinatorial Optimization and Applications, COCOA 2011, held in Zhangjiajie, China, in August 2011. The 43 revised full papers were carefully reviewed and selected from 65 submissions. The papers cover a broad range of topics in combinatorial optimization and applications focussing on experimental and applied research of general algorithmic interest and research motivated by real-world problems.

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Page Count

573

Publisher

Springer

Published Date

ISBN 10

3642226167

ISBN 13

9783642226168

Book's by Xuding Zhu

Combinatorial Nullstellensatz

Combinatorial Nullstellensatz

Combinatorial Nullstellensatz

Combinatorial Nullstellensatz

Combinatorial Optimization and Applications

Combinatorial Optimization and Applications

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