Combinatorial Nullstellensatz and DP-coloring of graphs

Anti-magic graphs via the Combinatorial NullStellenSatz

An antimagic labeling of a graph withm edges and n vertices is a bijection from the set of edges to the integers 1; . . . ;m such that all n vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges incident with that vertex. A graph is called antimagic if it has an antimagic labeling. In [10], Ringel conjectured that every simple connected graph, other than K2, is...

Combinatorial Nullstellensatz

We present a general algebraic technique and discuss some of its numerous applications in Combinatorial Number Theory, in Graph Theory and in Combinatorics. These applications include results in additive number theory and in the study of graph coloring problems. Many of these are known results, to which we present unified proofs, and some results are new.

Combinatorial Nullstellensatz

The Combinatorial Nullstellensatz is a theorem about the roots of a polynomial. It is related to Hilbert’s Nullstellensatz. Established in 1996 by Alon et al. [4] and generalized in 1999 by Alon [2], the Combinatorial Nullstellensatz is a powerful tool that allows the use of polynomials to solve problems in number theory and graph theory. This article introduces the Combinatorial Nullstellensat...

A Generalization of Combinatorial Nullstellensatz

In this note we give an extended version of Combinatorial Nullstellensatz, with weaker assumption on nonvanishing monomial. We also present an application of our result in a situation where the original theorem does not seem to work.

Applications of the Combinatorial Nullstellensatz