Polynomial-Size Enumeration Kernelizations for Long Path Enumeration
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912252315041792 |
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| author | Komusiewicz, Christian Majumdar, Diptapriyo Sommer, Frank |
| author_facet | Komusiewicz, Christian Majumdar, Diptapriyo Sommer, Frank |
| contents | Enumeration kernelization for parameterized enumeration problems was defined by Creignou et al. [Theory Comput. Syst. 2017] and was later refined by Golovach et al. [J. Comput. Syst. Sci. 2022, STACS 2021] to polynomial-delay enumeration kernelization. We consider ENUM LONG-PATH, the enumeration variant of the Long-Path problem, from the perspective of enumeration kernelization. Formally, given an undirected graph G and an integer k, the objective of ENUM LONG-PATH is to enumerate all paths of G having exactly k vertices. We consider the structural parameters vertex cover number, dissociation number, and distance to clique and provide polynomial-delay enumeration kernels of polynomial size for each of these parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21164 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polynomial-Size Enumeration Kernelizations for Long Path Enumeration Komusiewicz, Christian Majumdar, Diptapriyo Sommer, Frank Discrete Mathematics Enumeration kernelization for parameterized enumeration problems was defined by Creignou et al. [Theory Comput. Syst. 2017] and was later refined by Golovach et al. [J. Comput. Syst. Sci. 2022, STACS 2021] to polynomial-delay enumeration kernelization. We consider ENUM LONG-PATH, the enumeration variant of the Long-Path problem, from the perspective of enumeration kernelization. Formally, given an undirected graph G and an integer k, the objective of ENUM LONG-PATH is to enumerate all paths of G having exactly k vertices. We consider the structural parameters vertex cover number, dissociation number, and distance to clique and provide polynomial-delay enumeration kernels of polynomial size for each of these parameters. |
| title | Polynomial-Size Enumeration Kernelizations for Long Path Enumeration |
| topic | Discrete Mathematics |
| url | https://arxiv.org/abs/2502.21164 |