On vertex stability of complete k-partite graphs
Copyright policy )On vertex stability of complete k-partite graphs
Summary: 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 \textit{A. Dudek} and \textit{A. Żak} [Discuss. Math., Graph Theory 30, No. 4, 663--669 (2010; Zbl 1217.05112)] regarding complete bipartite graphs.
vertex stability, T57-57.97, Extremal problems in graph theory, Applied mathematics. Quantitative methods, Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.), complete \(k\)-partite graphs, minimal stable graphs
vertex stability, T57-57.97, Extremal problems in graph theory, Applied mathematics. Quantitative methods, Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.), complete \(k\)-partite graphs, minimal stable graphs
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