1st Edition
Combinatorial Nullstellensatz With Applications to Graph Colouring
Some definitions and notations. Combinatorial Nullstellensatz. Introduction. An application of CNS to additive number theory. Application of CNS to geometry. CNS and a subgraph problem. 0-1 vectors in a hyperplane. Alon-Tarsi Theorem and its Applications. Alon-Tarsi Theorem. Bipartite graphs and acyclic orientations. The Cartesian product of a path and an odd cycle. A solution to a problem of Erd˝os. Bound for AT (G) in terms of degree. Planar graphs. Planar graph minus a matching. Discharging method. Hypergraph colouring. Paintability of graphs. Generalizations of CNS and applications. Number of nonzero points. Multisets. Coefficient of a highest degree monomial. Calculation of NS(a). Alon-Tarsi number of K2*n and cycle powers. Alon-Tarsi numbers of toroidal grids. List colouring of line graphs. r-regular planar graphs. Complete graphs Kp+1 for odd prime p. Jaeger’s Conjecture. Permanent and vertex-edge weighting. Permanent as the coefficient. Edge weighting and total weighting. Polynomial associated to total weighting. Permanent index. Trees with an even number of edges. Complete graphs. Every graph is (2, 3)-choosable.
Biography
Xuding Zhu is currently a Professor of Mathematics, director of the Center for Discrete Mathematics at Zhejiang Normal University, China. His fields of interests are: Combinatorics and Graph Colouring. He published more than 260 research papers and served on the editorial board of SIAM Journal on Discrete Mathematics, Journal of Graph Theory, European Journal of Combinatorics, Electronic Journal of Combinatorics, Discrete Mathematics, Contribution to Discrete Mathematics, Discussion. Math. Graph Theory, Bulletin of Academia Sinica and Taiwanese Journal of Mathematics.
R. Balakrishnan is currently an Adjunct Professor of Mathematics at Bharathidasan University, Triuchirappalli, India. His fields of interests are: Algebraic Combinatorics and Graph Colouring. He is an author of three other books, one in Graph Theory and the other two in Discrete Mathematics. He is also one of the founders of the Ramanujan Mathematical Society and the Academy of Discrete Mathematics and Applications and currently an Editor-in-Chief of the Indian Journal of Discrete Mathematics.
