@Article{Nikodem2015,
author = "Nikodem, Mateusz",
title = "On vertex stability of complete k-partite graphs",
journal = "Opuscula Math.",
year = "2015",
volume = "35",
number = "6",
pages = "907--914",
doi = "http://dx.doi.org/10.7494/OpMath.2015.35.6.907",
url = "http://dx.doi.org/10.7494/OpMath.2015.35.6.907",
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",
issn = "1232-9274"
}