Reconfiguration of Minimum PSD Forcing Sets and Minimum Skew Forcing Sets
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915093468413952 |
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| author | Bong, Novi Flagg, Mary Hunnell, Mark Hutchens, John Moruzzi, Ryan Schuerger, Houston Small, Ben |
| author_facet | Bong, Novi Flagg, Mary Hunnell, Mark Hutchens, John Moruzzi, Ryan Schuerger, Houston Small, Ben |
| contents | Reconfiguration graphs provide a way to represent relationships among solutions to a problem, and have been studied in many contexts. We investigate the reconfiguration graphs corresponding to minimum PSD forcing sets and minimum skew forcing sets. We present results for the structure and realizability of certain graph classes as token exchange and token sliding reconfiguration graphs. Additionally, we use a universal approach to establish structural properties for the reconfiguration graphs of many common graph parameters under these reconfiguration rules. Finally, we compare results on reconfiguration graphs for zero forcing variants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reconfiguration of Minimum PSD Forcing Sets and Minimum Skew Forcing Sets Bong, Novi Flagg, Mary Hunnell, Mark Hutchens, John Moruzzi, Ryan Schuerger, Houston Small, Ben Combinatorics 05C50, 05C69, 05C57 Reconfiguration graphs provide a way to represent relationships among solutions to a problem, and have been studied in many contexts. We investigate the reconfiguration graphs corresponding to minimum PSD forcing sets and minimum skew forcing sets. We present results for the structure and realizability of certain graph classes as token exchange and token sliding reconfiguration graphs. Additionally, we use a universal approach to establish structural properties for the reconfiguration graphs of many common graph parameters under these reconfiguration rules. Finally, we compare results on reconfiguration graphs for zero forcing variants. |
| title | Reconfiguration of Minimum PSD Forcing Sets and Minimum Skew Forcing Sets |
| topic | Combinatorics 05C50, 05C69, 05C57 |
| url | https://arxiv.org/abs/2501.03642 |