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arXiv · 2411.19351

On the matching arrangement of a graph, improper weight function problem and its application

Aleksey Bolotnikov·Anwar Irmatov
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Abstract

This article presents examples of an application of the finite field method for the computation of the characteristic polynomial of the matching arrangement of a graph. Weight functions on edges of a graph with weights from a finite field are divided into proper and improper functions in connection with proper colorings of vertices of the matching polytope of a graph. An improper weight function problem is introduced, a proof of its NP-completeness is presented, and a knapsack-like public key cryptosystem is constructed based on the improper weight function problem.

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Aleksey Bolotnikov, Anwar Irmatov. 2025-01-22. On the matching arrangement of a graph, improper weight function problem and its application. https://arxiv.org/abs/2411.19351

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