Coloring linear hypergraphs: the Erdős–Faber–Lovász conjecture and the Combinatorial Nullstellensatz

on the effect of linear & non-linear texts on students comprehension and recalling

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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...

Applications of the Combinatorial Nullstellensatz

A Paintability Version of the Combinatorial Nullstellensatz, and List Colorings of k-partite k-uniform Hypergraphs

We study the list coloring number of k-uniform k-partite hypergraphs. Answering a question of Ramamurthi and West, we present a new upper bound which generalizes Alon and Tarsi’s bound for bipartite graphs, the case k = 2. Our results hold even for paintability (on-line list colorability). To prove this additional strengthening, we provide a new subject-specific version of the Combinatorial Nul...