Maximal k-independent sets in graphs
نویسندگان
چکیده
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 βj(G) and between ik(G) and ij(G) for j 6= 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.
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عنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 28 شماره
صفحات -
تاریخ انتشار 2008