Geodesic
Maximal k-independent sets in graphs
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 1, pp. 151-163.

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A subset of vertices of a graph G is k-independent if it induces in G a subgraph of maximum degree less than k. The minimum and maximum cardinalities of a maximal k-independent set are respectively denoted iₖ(G) and βₖ(G). We give some relations between βₖ(G) and β_j(G) and between iₖ(G) and i_j(G) for j ≠ k. We study two families of extremal graphs for the inequality i₂(G) ≤ i(G) + β(G). Finally we give an upper bound on i₂(G) and a lower bound when G is a cactus.
Keywords: k-independent, cactus 
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Blidia, Mostafa; Chellali, Mustapha; Favaron, Odile; Meddah, Nacéra. Maximal k-independent sets in graphs. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 1, pp. 151-163. http://geodesic.mathdoc.fr/item/DMGT_2008_28_1_a10/

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