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${session.getAttribute("locale")}5Cuntz-Kreiger algebras of infinite graphs and matrices
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Wed 11 Apr 2018 12:01:57 AEST]]>Sufficient conditions for graphs to be maximally 4-restricted edge connected
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k(G), is defined as the cardinality of a minimum k-restricted edge cut. A connected graph G is said to be λ_{k}-connected if G has a k-restricted edge cut. Let ξ_{k}(G) = min{|[X, ̅X ]| : |X| = k, G[X] is connected}, where ̅X = V (G)X. A graph G is said to be maximally k-restricted edge connected if λ_{k}(G) = ξ_{k}(G). In this paper we show that if G is a λ₄-connected graph with λ₄(G) ≤ ξ₄(G) and the girth satisfies g(G) ≥ 8, and there do not exist six vertices u₁, u₂, u₃, v₁, v₂ and v₃ in G such that the distance d(u_{i}, v_{j}) ≥ 3, (1 ≤ i, j ≤ 3), then G is maximally 4-restricted edge connected.]]>Tue 03 Sep 2019 18:17:58 AEST]]>