Invariant systems of weighted representatives
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911463287816192 |
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| author | Klyachko, Anton A. Terekhov, Mikhail S. |
| author_facet | Klyachko, Anton A. Terekhov, Mikhail S. |
| contents | It is known that, if removing some $n$ edges from a graph $Γ$ destroys all subgraphs isomorphic to a given finite graph $K$, then all subgraphs isomorphic to $K$ can be destroyed by removing at most $|E(K)|\cdot n$ edges, which form a set invariant with respect to all automorphisms of $Γ$. We construct the first examples of (connected) graphs $K$ for which this estimate is not sharp. Our arguments are based on a ``weighted analogue'' of an earlier known estimate for the cost of symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_11883 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Invariant systems of weighted representatives Klyachko, Anton A. Terekhov, Mikhail S. Combinatorics Group Theory It is known that, if removing some $n$ edges from a graph $Γ$ destroys all subgraphs isomorphic to a given finite graph $K$, then all subgraphs isomorphic to $K$ can be destroyed by removing at most $|E(K)|\cdot n$ edges, which form a set invariant with respect to all automorphisms of $Γ$. We construct the first examples of (connected) graphs $K$ for which this estimate is not sharp. Our arguments are based on a ``weighted analogue'' of an earlier known estimate for the cost of symmetry. |
| title | Invariant systems of weighted representatives |
| topic | Combinatorics Group Theory |
| url | https://arxiv.org/abs/2306.11883 |