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Minimally (k, k)Edge Connected Graphs
, 2001
"... Abstract: For an integer l> 1, the ledgeconnectivity of a connected graph with at least l vertices is the smallest number of edges whose removal results in a graph with l components. A connected graph G is (k; l)edgeconnected if the ledgeconnectivity of G is at least k. In this paper, we pr ..."
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Abstract: For an integer l> 1, the ledgeconnectivity of a connected graph with at least l vertices is the smallest number of edges whose removal results in a graph with l components. A connected graph G is (k; l)edgeconnected if the ledgeconnectivity of G is at least k. In this paper, we
Minimally kedgeconnected directed graphs of maximal size
, 2002
"... Minimally kedgeconnected directed graphs of maximal size ..."
ON CRITICALLY kEDGECONNECTED GRAPHS
"... Abstract: Let G be a simple graph on n vertices having edgeconnectivity /(. ' (G)> a and minimum degree o(G) We say G is kcritical if /(. ' (G) = k and /(. ' (G e) < k for every edge e of G. In this paper we prove that a kcritical graph has 1< ' (G) o(G). We descri ..."
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Abstract: Let G be a simple graph on n vertices having edgeconnectivity /(. ' (G)> a and minimum degree o(G) We say G is kcritical if /(. ' (G) = k and /(. ' (G e) < k for every edge e of G. In this paper we prove that a kcritical graph has 1< ' (G) o(G). We descri
Minimally (k, k)edgeconnected graphs
, 2002
"... For an integer l> 1, the ledgeconnectivity of a connected graph with at least l vertices is the smallest number of edges whose removal results in a graph with l components. A connected graph G is (k, l)edgeconnected if the ledgeconnectivity of G is at least k. In this paper we present a str ..."
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Cited by 1 (0 self)
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For an integer l> 1, the ledgeconnectivity of a connected graph with at least l vertices is the smallest number of edges whose removal results in a graph with l components. A connected graph G is (k, l)edgeconnected if the ledgeconnectivity of G is at least k. In this paper we present a
Parity Constrained kEdgeConnected Orientations
, 1999
"... Parity (matching theory) and connectivity (network flows) are two main branches of combinatorial optimization. In an attempt to understand better their interrelation, we study a problem where both parity and connectivity requirements are imposed. The main result is a characterization of undirected g ..."
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Cited by 4 (2 self)
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graphs G = (V; E) having a kedgeconnected T odd orientation for every subset T ` V with jEj + jT j even. (T odd orientation: the indegree of v is odd precisely if v is in T .) As a corollary, we obtain that every (2k + 2)edgeconnected graph with jV j + jEj even has a kedgeconnected orientation
Range assignment for biconnectivity and kedge connectivity in wireless ad hoc networks
 MONET
"... Abstract. Depending on whether bidirectional links or unidirectional links are used for communications, the network topology under a given range assignment is either an undirected graph referred to as the bidirectional topology, or a directed graph referred to as the unidirectional topology. The Min ..."
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Cited by 12 (0 self)
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. The MinPower Bidirectional (resp., Unidirectional) kNode Connectivity problem seeks a range assignment of minimum total power subject to the constraint that the produced bidirectional (resp. unidirectional) topology is kvertex connected. Similarly, the MinPower Bidirectional (resp., Unidirectional) kEdge
On Minimum kEdgeConnectivity Augmentation for Specified
, 2006
"... SUMMARY The kedgeconnectivity augmentation problem for a specified set of vertices of a graph with degree constraints, kECASVDC, is defined as follows: “Given an undirected multigraph G = (V, E), a specified set of vertices S ⊆ V and a function g: V → Z + ∪{∞}, find a smallest set E ′ of edges s ..."
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SUMMARY The kedgeconnectivity augmentation problem for a specified set of vertices of a graph with degree constraints, kECASVDC, is defined as follows: “Given an undirected multigraph G = (V, E), a specified set of vertices S ⊆ V and a function g: V → Z + ∪{∞}, find a smallest set E ′ of edges
VERTICES OF DEGREE k IN EDGEMINIMAL, kEDGECONNECTED GRAPHS
, 2009
"... Halin [1] showed that every edgeminimal, kvertexconnected graph has a vertex of degree k. In this note, we prove the analogue to Halin's theorem for edgeminimal, kedgeconnected graphs: Theorem 1. Let G be an edgeminimal, kedgeconnected graph. Then there are two nodes of degree k in G. ..."
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Halin [1] showed that every edgeminimal, kvertexconnected graph has a vertex of degree k. In this note, we prove the analogue to Halin's theorem for edgeminimal, kedgeconnected graphs: Theorem 1. Let G be an edgeminimal, kedgeconnected graph. Then there are two nodes of degree k in G
Results 1  10
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644,842