The cost of symmetry for tailed stars
Abstract
It is known that if n vertices can be removed from a connected graph so that no subgraphs isomorphic to the graph K remain, then no more than |V(K)|· n vertices can be removed, forming a set invariant with respect to all automorphisms of the graph , 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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