Strong Subgraph $k$-connectivity
نویسندگان
چکیده
Generalized connectivity introduced by Hager (1985) has been studied extensively in undirected graphs and become an established area in undirected graph theory. For connectivity problems, directed graphs can be considered as generalizations of undirected graphs. In this paper, we introduce a natural extension of generalized k-connectivity of undirected graphs to directed graphs (we call it strong subgraph kconnectivity) by replacing connectivity with strong connectivity. We prove NP-completeness results and the existence of polynomial algorithms. We show that strong subgraph k–connectivity is, in a sense, harder to compute than generalized k-connectivity. However, strong subgraph k-connectivity can be computed in polynomial time for semicomplete digraphs and symmetric digraphs. We also provide sharp bounds on strong subgraph k-connectivity and pose some open questions.
منابع مشابه
Strong subgraph $k$-connectivity bounds
Let D = (V,A) be a digraph of order n, S a subset of V of size k and 2 ≤ k ≤ n. Strong subgraphs D1, . . . , Dp containing S are said to be internally disjoint if V (Di)∩V (Dj) = S and A(Di)∩A(Dj) = ∅ for all 1 ≤ i < j ≤ p. Let κS(D) be the maximum number of internally disjoint strong digraphs containing S in D. The strong subgraph kconnectivity is defined as κk(D) = min{κS(D) | S ⊆ V, |S| = k}...
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