Validating a PTAS for Triangle-Free 2-Matching via a Simple Decomposition Theorem
Data Structures and Algorithms
2024-10-24 v1
Abstract
A triangle-free (simple) 2-matching is an edge set that has at most edges incident to each vertex and contains no cycle of length . For the problem of finding a maximum cardinality triangle-free 2-matching in a given graph, a complicated exact algorithm was proposed by Hartvigsen. Recently, a simple PTAS using local search was presented by Bosch-Calvo, Grandoni, and Ameli, but its validity proof is not easy. In this paper, we show a natural and simple decomposition theorem for triangle-free 2-matchings, which leads to a simpler validity proof of the PTAS for the problem.
Cite
@article{arxiv.2410.17508,
title = {Validating a PTAS for Triangle-Free 2-Matching via a Simple Decomposition Theorem},
author = {Yusuke Kobayashi and Takashi Noguchi},
journal= {arXiv preprint arXiv:2410.17508},
year = {2024}
}