Opuscula Math. 35, no. 6 (2015), 907-914

Opuscula Mathematica

On vertex stability of complete k-partite graphs

Mateusz Nikodem

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.

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  • Mateusz Nikodem
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland
  • Received: 2013-12-10.
  • Revised: 2015-01-19.
  • Accepted: 2015-03-16.
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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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