Catalog > Sciences > Math > R. Balakrishnan & Xuding Zhu: Combinatorial Nullstellensatz (ePUB)

R. Balakrishnan & Xuding Zhu
Combinatorial Nullstellensatz [EPUB ebook]
With Applications to Graph Colouring

Support

Cover of R. Balakrishnan & Xuding Zhu: Combinatorial Nullstellensatz (ePUB)

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.

€25.62

Buy this ebook and get 1 more FREE!

Format EPUB ● Pages 150 ● ISBN 9781000426694 ● Publisher CRC Press ● Published 2021 ● Downloadable 3 times ● Currency EUR ● ID 7853273 ● Copy protection Adobe DRM

Requires a DRM capable ebook reader

More ebooks from the same author(s) / Editor

R. Balakrishnan Xuding Zhu

48,795 Ebooks in this category

Cover of Richard A. Mollin: Quadratics

Richard A. Mollin: Quadratics

The first thing you will find out about this book is that it is fun to read. It is meant for the browser, as well as for the student and for the specialist wanting to know about the area. The footnot …

Cover of Peter B. (University of Oregon, Eugene, USA) Gilkey: Invariance Theory

Peter B. (University of Oregon, Eugene, USA) Gilkey: Invariance Theory

This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz f …

Cover of V. Balakrishnan: Network Optimization

V. Balakrishnan: Network Optimization

Problems in network optimization arise in all areas of technology and industrial management. The topic of network flows has applications in diverse fields such as chemistry, engineering, management s …

Cover of John Bird: Mathematics Pocket Book for Engineers and Scientists

John Bird: Mathematics Pocket Book for Engineers and Scientists

This compendium of essential formulae, definitions, tables and general information provides the mathematical information required by engineering students, technicians, scientists and professionals in …

Cover of Jeffrey Holt: Linear Algebra

Jeffrey Holt: Linear Algebra

Now in its 2nd edition, Linear Algebra with Applications blends computational and conceptual topics to prepare students for the rigors of conceptual thinking in an abstract setting. The early treatme …

Cover of David J. (Naval Surface Warfare Center, Dahlgren, Virginia, USA) Marchette & Rakesh M. (University of Houston, Texas, USA) Verma: Cybersecurity Analytics

David J. (Naval Surface Warfare Center, Dahlgren, Virginia, USA) Marchette & Rakesh M. (University of Houston, Texas, USA) Verma: Cybersecurity Analytics

Cybersecurity Analytics is for the cybersecurity student and professional who wants to learn data science techniques critical for tackling cybersecurity challenges, and for the data science student a …

Cover of Peter Sprent: Data Driven Statistical Methods

Peter Sprent: Data Driven Statistical Methods

Calculations once prohibitively time-consuming can be completed in microseconds by modern computers. This has resulted in dramatic shifts in emphasis in applied statistics. Not only has it freed us f …

Cover of John J. Benedetto: Harmonic Analysis and Applications

John J. Benedetto: Harmonic Analysis and Applications

Harmonic analysis plays an essential role in understanding a host of engineering, mathematical, and scientific ideas. In Harmonic Analysis and Applications, the analysis and synthesis of functions in …

Cover of Daniel Lesnic: Inverse Problems with Applications in Science and Engineering

Daniel Lesnic: Inverse Problems with Applications in Science and Engineering

Driven by the advancement of industrial mathematics and the need for impact case studies, Inverse Problems with Applications in Science and Engineering thoroughly examines the state-of-the-art of som …

Cover of Barry Parker: Isaac Newton School Driving

Barry Parker: Isaac Newton School Driving

“Wonderful . . . a great resource for automobile fans who want to understand science, and vice versa.” —Alan C. Tribble, author of A Tribble’s Guide to Space For some, driving is an ar …