Independent set reconfiguration in H-free graphs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916115625541632 |
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| author | Bartier, Valentin Bousquet, Nicolas Mühlenthaler, Moritz |
| author_facet | Bartier, Valentin Bousquet, Nicolas Mühlenthaler, Moritz |
| contents | Given a graph $G$ and two independent sets of $G$, the independent set reconfiguration problem asks whether one independent set can be transformed into the other by moving a single vertex at a time, such that at each intermediate step we have an independent set of $G$. We study the complexity of this problem for $H$-free graphs under the token sliding and token jumping rule. Our contribution is twofold. First, we prove a reconfiguration analogue of Alekseev's theorem, showing that the problem is PSPACE-complete unless $H$ is a path or a subdivision of the claw. We then show that under the token sliding rule, the problem admits a polynomial-time algorithm if the input graph is fork-free. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03063 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Independent set reconfiguration in H-free graphs Bartier, Valentin Bousquet, Nicolas Mühlenthaler, Moritz Discrete Mathematics Data Structures and Algorithms Given a graph $G$ and two independent sets of $G$, the independent set reconfiguration problem asks whether one independent set can be transformed into the other by moving a single vertex at a time, such that at each intermediate step we have an independent set of $G$. We study the complexity of this problem for $H$-free graphs under the token sliding and token jumping rule. Our contribution is twofold. First, we prove a reconfiguration analogue of Alekseev's theorem, showing that the problem is PSPACE-complete unless $H$ is a path or a subdivision of the claw. We then show that under the token sliding rule, the problem admits a polynomial-time algorithm if the input graph is fork-free. |
| title | Independent set reconfiguration in H-free graphs |
| topic | Discrete Mathematics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2402.03063 |