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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.17508 |
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| _version_ | 1866913560874975232 |
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| author | Kobayashi, Yusuke Noguchi, Takashi |
| author_facet | Kobayashi, Yusuke Noguchi, Takashi |
| contents | A triangle-free (simple) 2-matching is an edge set that has at most $2$ edges incident to each vertex and contains no cycle of length $3$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17508 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Validating a PTAS for Triangle-Free 2-Matching via a Simple Decomposition Theorem Kobayashi, Yusuke Noguchi, Takashi Data Structures and Algorithms A triangle-free (simple) 2-matching is an edge set that has at most $2$ edges incident to each vertex and contains no cycle of length $3$. 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. |
| title | Validating a PTAS for Triangle-Free 2-Matching via a Simple Decomposition Theorem |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2410.17508 |