Opuscula Mathematica
Opuscula Math. 35, no. 6 (), 907-914
Opuscula Mathematica

On vertex stability of complete k-partite graphs

Abstract. Let \(H\) be any graph. We say that graph \(G\) is \(H\)-stable if \(G-u\) contains a subgraph isomorphic to \(H\) for an arbitrary chosen \(u\in V(G)\). We characterize all \(H\)-stable graphs of minimal size where \(H\) is any complete \(k\)-partite graph. Thus, we generalize the results of Dudek and Żak regarding complete bipartite graphs.
Keywords: vertex stability, minimal stable graphs, complete \(k\)-partite graphs.
Mathematics Subject Classification: 05C35, 05C60.
Cite this article as:
Mateusz Nikodem, On vertex stability of complete k-partite graphs, Opuscula Math. 35, no. 6 (2015), 907-914, http://dx.doi.org/10.7494/OpMath.2015.35.6.907
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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