دانلود کتاب Combinatorial Nullstellensatz

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Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
Authors
Acknowledgements
1. Some Definitions and Notations
2. Combinatorial Nullstellensatz
2.1. Introduction
2.2. An application of CNS to additive number theory
2.3. Application of CNS to geometry
2.4. CNS and a subgraph problem
2.5. 0-1 vectors in a hyperplane
3. Alon–Tarsi Theorem and Its Applications
3.1. Alon-Tarsi theorem
3.2. Bipartite graphs and acyclic orientations
3.3. The Cartesian product of a path and an odd cycle
3.4. A solution to a problem of Erd}os
3.5. Bound for AT(G) in terms of degree
3.6. Planar graphs
3.7. Planar graph minus a matching
3.8. Discharging method
3.9. Hypergraph colouring
3.10. Paintability of graphs
4. Generalizations of CNS and Applications
4.1. Number of non-zero points
4.2. Multisets
4.3. Coefficient of a highest degree monomial
4.4. Calculation of NS(a)
4.5. Alon-Tarsi number of K 2*n and cycle powers
4.6. Alon-Tarsi numbers of toroidal grids
4.7. List colouring of line graphs
4.8. r-regular planar graphs
4.9. Complete graphs K p+1 for odd prime p
4.10. Jaeger\'s conjecture
5. Permanent and Vertex-edge Weighting
5.1. Permanent as the coefficient
5.2. Edge weighting and total weighting
5.3. Polynomial associated to total weighting
5.4. Permanent index
5.5. Trees with an even number of edges
5.6. Complete graphs
5.7. Every graph is (2,3)-choosable
Bibliography
Index