Cs 598csc: Approximation Algorithms 1 Graph Orientation
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چکیده
Proof: “⇒” Suppose D = (V,A) is a strongly connected graph obtained as an orientation of G = (V,E). Then, since ∀S ⊂ V , |δ D(S)| ≥ 1 and |δ − D(S)| ≥ 1, we have |δG(S)| ≥ 2. Therefore, G is 2-edge-connected. “⇐” Let G be a 2-edge-connected graph. Then G has an ear-decomposition. In other words, G is either a cycle C or G is obtained from a 2-edge-connected graph G by adding an ear P (a path) connecting two not-necessarily distinct vertices u, v ∈ V .
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