English

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

Combinatorics 2025-01-23 v3 Cryptography and Security Discrete Mathematics

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.

Keywords

Cite

@article{arxiv.2411.19351,
  title  = {On the matching arrangement of a graph, improper weight function problem and its application},
  author = {Aleksey Bolotnikov and Anwar Irmatov},
  journal= {arXiv preprint arXiv:2411.19351},
  year   = {2025}
}
R2 v1 2026-06-28T20:16:14.793Z