# Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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# $(C_n;k)$ - stable graphs with minimum size

Presented by Agnieszka GöRLICH
Type: Oral presentation
Track: General session

## Content

A graph $G$ is called $(H;k)$ - {\it vertex stable} if $G$ contains a subgraph isomorphic to $H$ ever after removing any of its $k$ vertices; stab$(H;k)$ denotes the minimum size among the sizes of all $(H;k)$ - vertex stable graphs. We show that stab $(C_{n};1)$ is one of only two possible values for each $n$ and we give the exact value for infinitely many $n$'s. Furthermore we establish an upper and lower bound for stab $(C_{n};k)$ for $k\geq 2$.

## Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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