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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.03746 |
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| _version_ | 1866915934258593792 |
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| author | Terekhov, M. S. |
| author_facet | Terekhov, M. S. |
| contents | It is known that if $n$ vertices can be removed from a connected graph $Γ$ so that no subgraphs isomorphic to the graph $K$ remain, then no more than $|V(K)|\cdot n$ vertices can be removed, forming a set invariant with respect to all automorphisms of the graph $Γ$, so that no subgraphs isomorphic to the graph $K$ remain. We construct an infinite set of (connected) graphs $K$ for which this estimate is not exact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03746 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The cost of symmetry for tailed stars Terekhov, M. S. Combinatorics It is known that if $n$ vertices can be removed from a connected graph $Γ$ so that no subgraphs isomorphic to the graph $K$ remain, then no more than $|V(K)|\cdot n$ vertices can be removed, forming a set invariant with respect to all automorphisms of the graph $Γ$, so that no subgraphs isomorphic to the graph $K$ remain. We construct an infinite set of (connected) graphs $K$ for which this estimate is not exact. |
| title | The cost of symmetry for tailed stars |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.03746 |