Results 11 to 20 of about 1,715 (93)
Residues and the Combinatorial Nullstellensatz [PDF]
Periodica Mathematica Hungarica, 2018 We interpret the Combinatorial Nullstellensatz of Noga Alon as a multidimensional residue formula, describe some consequences of this interpretation and related open problems.
Roman Karasev
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Coloring linear hypergraphs: the Erdős–Faber–Lovász conjecture and the Combinatorial Nullstellensatz [PDF]
Designs, Codes and Cryptography, 2021 AbstractThe long-standing Erdős–Faber–Lovász conjecture states that every n-uniform linear hypergaph with n edges has a proper vertex-coloring using n colors. In this paper we propose an algebraic framework to the problem and formulate a corresponding stronger conjecture.
Oliver Janzer, Zoltán Lóránt Nagy
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4-choosability of planar graphs with 4-cycles far apart via the Combinatorial Nullstellensatz
Discrete Mathematics, 2023 By a well-known theorem of Thomassen and a planar graph depicted by Voigt, we know that every planar graph is $5$-choosable, and the bound is tight. In 1999, Lam, Xu and Liu reduced $5$ to $4$ on $C_4$-free planar graphs. In the paper, by applying the famous Combinatorial Nullstellensatz, we design an effective algorithm to deal with list coloring ...
Fan Yang, Yue Wang, Jian-Liang Wu
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Computing infeasibility certificates for combinatorial problems through Hilbert’s Nullstellensatz
Journal of Symbolic Computation, 2011 Systems of polynomial equations over a field can yield compact models of difficult combinatorial problems and they can be used to prove combinatorial results. In particular, existence of the solutions of the systems means that the combinatorial objects have the properties captured by the systems.
De Loera, Jesús A. +3 more
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Combinatorial Nullstellensatz approach to polynomial expansion
Acta Arithmetica, 2014 Applying techniques similar to Combinatorial Nullstellensatz we prove a lower estimate of $|f(A,B)|$ for finite subsets $A$, $B$ of a field, and polynomial $f(x,y)$ of the form $f(x,y)=g(x)+yh(x)$, where degree of $g$ is greater then degree of $h$.
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A Combinatorial Proof of the Effective Nullstellensatz
Journal of Symbolic Computation, 1993 The degree bound in the effective Nullstellensatz is obtained using combinatorial methods, namely counting arguments for the ideal \(I\).
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Neighbour sum distinguishing total colourings via the Combinatorial Nullstellensatz
Discrete Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jakub Przybyło
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Combinatorial Nullstellensatz and Turán numbers of complete r-partite r-uniform hypergraphs
Discrete Mathematics3 ...
Alexey Gordeev
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Weak sequenceability in cyclic groups
Journal of Combinatorial Designs, Volume 30, Issue 12, Page 735-751, December 2022., 2022 Abstract A subset A $A$ of an abelian group G $G$ is sequenceable if there is an ordering ( a 1 , … , a k ) $({a}_{1},\ldots ,{a}_{k})$ of its elements such that the partial sums ( s 0 , s 1 , … , s k ) $({s}_{0},{s}_{1},\ldots ,{s}_{k})$, given by s 0 = 0 ${s}_{0}=0$ and s i = ∑ j = 1 i a j ${s}_{i}={\sum }_{j=1}^{i}{a}_{j}$ for 1 ≤ i ≤ k $1\le i\le k$
Simone Costa, Stefano Della Fiore
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Between proper and strong edge‐colorings of subcubic graphs
Journal of Graph Theory, Volume 101, Issue 4, Page 686-716, December 2022., 2022 Abstract In a proper edge‐coloring the edges of every color form a matching. A matching is induced if the end‐vertices of its edges induce a matching. A strong edge‐coloring is an edge‐coloring in which the edges of every color form an induced matching.
Herve Hocquard +2 more
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