Geodesic
On \((C_n;k)\) stable graphs
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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A graph $G$ is called $(H;k)$-vertex stable if $G$ contains a subgraph isomorphic to $H$ ever after removing any $k$ of its vertices; stab$(H;k)$ denotes the minimum size among the sizes of all $(H;k)$-vertex stable graphs. In this paper we deal with $(C_{n};k)$-vertex stable graphs with minimum size. For each $n$ we prove that stab$(C_{n};1)$ is one of only two possible values 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 $k\geq 2$.
DOI : 10.37236/692
Classification : 05C35
Mots-clés : \((H, k)\)-vertex stable graph 
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     author = {Sylwia Cichacz and Agnieszka G\"orlich and Magorzata Zwonek and Andrzej \.Zak},
     title = {On {\((C_n;k)\)} stable graphs},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/692},
     zbl = {1229.05136},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/692/}
}
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Sylwia Cichacz; Agnieszka Görlich; Magorzata Zwonek; Andrzej Żak. On \((C_n;k)\) stable graphs. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/692

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