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arXiv · 2510.03746

The cost of symmetry for tailed stars

M. S. Terekhov
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Abstract

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.

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M. S. Terekhov. 2026-04-13. The cost of symmetry for tailed stars. https://arxiv.org/abs/2510.03746

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