Results 11 to 20 of about 107 (87)
Tropical Combinatorial Nullstellensatz and Sparse Polynomials [PDF]
Foundations of Computational Mathematics, 2019 Tropical algebra emerges in many fields of mathematics such as algebraic geometry, mathematical physics and combinatorial optimization. In part, its importance is related to the fact that it makes various parameters of mathematical objects computationally accessible.
Dima Grigoriev, Vladimir V. Podolskii
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Additive List Coloring of Planar Graphs with Given Girth
Discussiones Mathematicae Graph Theory, 2020 An additive coloring of a graph G is a labeling of the vertices of G from {1, 2, . . . , k} such that two adjacent vertices have distinct sums of labels on their neighbors.
Brandt Axel +2 more
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A Generalization of Combinatorial Nullstellensatz [PDF]
The Electronic Journal of Combinatorics, 2010 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.
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Hilbert's nullstellensatz and an algorithm for proving combinatorial infeasibility [PDF]
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, 2008 Systems of polynomial equations over an algebraically-closed field K can be used to concisely model many combinatorial problems. In this way, a combinatorial problem is feasible (e.g., a graph is 3-colorable, hamiltonian, etc.) if and only if a related system of polynomial equations has a solution over K.
Jesús A. De Loera +3 more
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Neighbor Sum Distinguishing Total Choosability of IC-Planar Graphs
Discussiones Mathematicae Graph Theory, 2020 Two distinct crossings are independent if the end-vertices of the crossed pair of edges are mutually different. If a graph G has a drawing in the plane such that every two crossings are independent, then we call G a plane graph with independent crossings
Song Wen-Yao +2 more
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Combinatorial Nullstellensatz [PDF]
Combinatorics, Probability and Computing, 1999 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 colouring problems.
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Constructing integer-magic graphs via the Combinatorial Nullstellensatz
The Art of Discrete and Applied Mathematics, 2022 Summary: Let Abe a nontrivial abelian group and \(A^\ast = A \backslash \{0\}\). A graph is \(A\)-magic if there exists an edge labeling fusing elements of \(A^\ast\) which induces a constant vertex labeling of the graph. Such a labeling \(f\) is called an \(A\)-magic labeling and the constant value of the induced vertex labeling is called an \(A ...
Low, Richard M., Roberts, Dan
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A Duality Based Proof of the Combinatorial Nullstellensatz [PDF]
The Electronic Journal of Combinatorics, 2009 In this note we present a proof of the combinatorial nullstellensatz using simple arguments from linear algebra.
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A Gröbner Basis Approach to Combinatorial Nullstellensatz
, 2023 In this paper, using some conditions that arise naturally in Alon's combinatorial Nullstellensatz as well as its various extensions and generalizations, we characterize Gröbner bases consisting of monic polynomials, which helps us to establish a Nullstellensatz from a Gröbner basis perspective.
Xu, Yang, Kan, Haibin, Han, Guangyue
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Schwartz-Zippel bounds for two-dimensional products
Discrete Analysis, 2017 Schwartz-Zippel bounds for two-dimensional products, Discrete Analysis 2017:20, A famous open problem in combinatorial geometry is Erdős's unit-distances problem, which asks the following: given a subset $A\subset\mathbb R^2$ of size $n$, how many ...
Hossein Nassajian Mojarrad +3 more
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