On the b-Independence Number of Sparse Random Graphs
نویسندگان
چکیده
Let graph G = (V,E) and integer b ≥ 1 be given. A set S ⊆ V is said to be b-independent if u, v ∈ S implies dG(u, v) > b where dG(u, v) is the shortest distance between u and v in G. The b-independence number αb(G) is the size of the largest b-independent subset of G. When b = 1 this reduces to the standard definition of independence number. We study this parameter in relation to the random graph Gn,p, p = d/n. In particular, when d is a large constant. We show that whp that if d ≥ dǫ,b,
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عنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 13 شماره
صفحات -
تاریخ انتشار 2004