Apr 18, 2023 · For Polynomial Calculus, Nullstellensatz exp Ω𝑑𝑛 on special graph Lauria-Nordström'17, Atserias-Ochreimak'19. Ω(𝑔/𝜒) degree, 𝑔 is girth ...

In this work, we establish optimal, linear, degree lower bounds and exponential size lower bounds for polynomial calculus proofs of non-colourability of random ...

We prove that polynomial calculus (and hence also Nullstellensatz) over any field requires linear degree to refute that sparse random regular graphs.

I. INTRODUCTION. Determining the chromatic number of a graph G, i.e., how many colours are needed for the vertices of G if no two vertices.

May 31, 2023 · Abstract:We consider the graph k-colouring problem encoded as a set of polynomial equations in the standard way over 0/1-valued variables.

We prove that polynomial calculus (and hence also Nullstellensatz) over any field requires linear degree to refute that sparse random regular graphs, as well as ...

Graph Colouring Is Hard on Average for Polynomial Calculus and Nullstellensatz ... We study the graph coloring problem over random graphs of finite average ...

It is proved that there are bounded-degree graphs that do not have legal k-colourings but for which the polynomial calculus proof system requires linear degree.

Graph Colouring Is Hard on Average for Polynomial Calculus and Nullstellensatz. J Conneryd, SF De Rezende, J Nordström, S Pang, K Risse. 2023 IEEE 64th Annual ...

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