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On connected \((\gamma,k)\)-critical graphs. (English) Zbl 1196.05064

Summary: A graph \(G\) is said to be \((\gamma,k)\)-critical if \(\gamma(G-S)<\gamma(G)\) for any set \(S\) of \(k\) vertices and domination number \(\gamma\). Properties of \((\gamma,k)\)-critical graphs are studied for \(k \geq 3\). Ways of constructing a \((\gamma,k)\)-critical graph from smaller \((\gamma,k)\)-critical graphs are presented.

MSC:

05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C35 Extremal problems in graph theory
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