Degree conditions for graphs to be maximally k-restricted edge connected and super k-restricted edge connected
نویسندگان
چکیده
منابع مشابه
Sufficient conditions for maximally edge-connected and super-edge-connected
Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...
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For a connected graph G = (V , E), an edge set S ⊂ E is a k-restricted edge cut if G − S is disconnected and every component of G − S contains at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is defined as the cardinality of a minimum krestricted edge cut. For U1,U2 ⊂ V (G), denote the set of edges of Gwith one end in U1 and the other in U2 by [U1,U2]. Define ξk(G...
متن کاملmaximally edge - connected and super - edge - connected graphs ∗
Let G be a connected graph with minimum degree δ and edgeconnectivity λ. A graph is maximally edge-connected if λ = δ, and it is superedge-connected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. In this paper, we show that a connected graph or a connected triangle-free graph is maximally edge-connected or sup...
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For a subset S of edges in a connected graph G, the set S is a k-restricted edge cut if G− S is disconnected and every component of G− S has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is defined as the cardinality of a minimum k-restricted edge cut. A connected graph G is said to be λk-connected if G has a k-restricted edge cut. Let ξk(G) = min{|[X, X̄ ]| : |...
متن کاملMinimally (k, k-1)-edge-connected graphs
For an interger l > 1, the l-edge-connectivity λl(G) of G is defined to be the smallest number of edges whose removal leaves a graph with at least l components, if |V (G)| ≥ l; and λl(G) = |V (G)| if |V (G)| ≤ l. A graph G is (k, l)-edge-connected if the l-edge-connectivity of G is at least k. A sufficient and necessary condition for G to be minimally (k, k − 1)-edgeconnected is obtained in the...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2015
ISSN: 0166-218X
DOI: 10.1016/j.dam.2014.10.027