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Quadrangularly connected clawfree graphs
"... A graph G is quadrangularly connected if for every pair of edges e1 and e2 in E(G), G has a sequence of lcycles (3 ≤ l ≤ 4) C1, C2,..., Cr such that e1 ∈ E(C1) and e2 ∈ E(Cr) and E(Ci) ∩ E(Ci+1) � = ∅ for i = 1, 2,..., r − 1. In this paper, we show that every quadrangularly connected clawfree gr ..."
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Cited by 1 (1 self)
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A graph G is quadrangularly connected if for every pair of edges e1 and e2 in E(G), G has a sequence of lcycles (3 ≤ l ≤ 4) C1, C2,..., Cr such that e1 ∈ E(C1) and e2 ∈ E(Cr) and E(Ci) ∩ E(Ci+1) � = ∅ for i = 1, 2,..., r − 1. In this paper, we show that every quadrangularly connected clawfree
Path extendability of clawfree graphs
, 2006
"... Let G be a connected, locally connected, clawfree graph of order n and x,y be two vertices of G. In this paper, we prove that if for any 2cut S of G, S ∩{x,y}=∅, then each (x, y)path of length less than n − 1inG is extendable, that is, for any path P joining x and y of length h(< n − 1), there ..."
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Let G be a connected, locally connected, clawfree graph of order n and x,y be two vertices of G. In this paper, we prove that if for any 2cut S of G, S ∩{x,y}=∅, then each (x, y)path of length less than n − 1inG is extendable, that is, for any path P joining x and y of length h(< n − 1
Clawfree Graphs. III. Circular interval graphs
, 2007
"... Construct a graph as follows. Take a circle, and a collection of intervals from it, no three of which have union the entire circle; take a finite set of points V from the circle; and make a graph with vertex set V in which two vertices are adjacent if they both belong to one of the intervals. Such g ..."
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Cited by 13 (6 self)
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graphs. This paper also gives an analysis of the clawfree graphs G with a clique the deletion of which disconnects G into two parts both with at least two vertices.
On stable cutsets in clawfree graphs and planar graphs
, 2008
"... A stable cutset in a connected graph is a stable set whose deletion disconnects the graph. Let K4 and K1,3 (claw) denote the complete (bipartite) graph on 4 and 1 + 3 vertices. It is NPcomplete to decide whether a line graph (hence a clawfree graph) with maximum degree five or a K4free graph admi ..."
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Cited by 3 (1 self)
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A stable cutset in a connected graph is a stable set whose deletion disconnects the graph. Let K4 and K1,3 (claw) denote the complete (bipartite) graph on 4 and 1 + 3 vertices. It is NPcomplete to decide whether a line graph (hence a clawfree graph) with maximum degree five or a K4free graph
Spanning Eulerian Subgraphs in clawfree graphs
"... A graph is clawfree if it has no induced K1,3 subgraph. A graph is essential 4edgeconnected if removing at most three edges, the resulting graph has at most one component having edges. In this note, we show that every essential 4edgeconnected claw free graph has a spanning Eulerian subgraph with ..."
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Cited by 1 (1 self)
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A graph is clawfree if it has no induced K1,3 subgraph. A graph is essential 4edgeconnected if removing at most three edges, the resulting graph has at most one component having edges. In this note, we show that every essential 4edgeconnected claw free graph has a spanning Eulerian subgraph
On disconnected cuts and separators
 Discrete Applied Mathematics 159
"... Abstract. For a connected graph G = (V, E), a subset U ⊆ V is called a disconnected cut if U disconnects the graph and the subgraph induced by U is disconnected as well. A natural condition is to impose that for any u ∈ U the subgraph induced by (V \U ) ∪ {u} is connected. In that case U is called ..."
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Cited by 1 (0 self)
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Abstract. For a connected graph G = (V, E), a subset U ⊆ V is called a disconnected cut if U disconnects the graph and the subgraph induced by U is disconnected as well. A natural condition is to impose that for any u ∈ U the subgraph induced by (V \U ) ∪ {u} is connected. In that case U is called
The computational complexity of disconnected cut and 2k2partition
 CoRR
, 2011
"... For a connected graph G = (V,E), a subset U ⊆ V is called a disconnected cut if U disconnects the graph and the subgraph induced by U is disconnected as well. We show that the problem to test whether a graph has a disconnected cut is NPcomplete. This problem is polynomially equivalent to the follow ..."
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Cited by 6 (2 self)
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For a connected graph G = (V,E), a subset U ⊆ V is called a disconnected cut if U disconnects the graph and the subgraph induced by U is disconnected as well. We show that the problem to test whether a graph has a disconnected cut is NPcomplete. This problem is polynomially equivalent
An improved approximation algorithm for multiway cut
 Journal of Computer and System Sciences
, 1998
"... Given an undirected graph with edge costs and a subset of k nodes called terminals, a multiway cut is a subset of edges whose removal disconnects each terminal from the rest. Multiway Cut is the problem of finding a multiway cut of minimum cost. Previously, a very simple combinatorial algorithm due ..."
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Cited by 71 (5 self)
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Given an undirected graph with edge costs and a subset of k nodes called terminals, a multiway cut is a subset of edges whose removal disconnects each terminal from the rest. Multiway Cut is the problem of finding a multiway cut of minimum cost. Previously, a very simple combinatorial algorithm due
4restricted edge cuts of graphs
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 30 (2004), PAGES 103–112
, 2004
"... A 4restricted edge cut is an edge cut of a connected graph which disconnects the graph, where each component has order at least 4. Graphs that contain 4restricted edge cuts are characterized in this paper. As a result, it is proved that a connected graph G of order at least 10 contains 4restricte ..."
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A 4restricted edge cut is an edge cut of a connected graph which disconnects the graph, where each component has order at least 4. Graphs that contain 4restricted edge cuts are characterized in this paper. As a result, it is proved that a connected graph G of order at least 10 contains 4
Approximation algorithms for requirement cut on graphs
 In APPROX + RANDOM
, 2005
"... In this paper, we unify several graph partitioning problems including multicut, multiway cut, and kcut, into a single problem. The input to the requirement cut problem is an undirected edgeweighted graph G = (V, E), and g groups of vertices X1, · · · , Xg ⊆ V, with each group Xi having a requir ..."
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Cited by 9 (2 self)
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In this paper, we unify several graph partitioning problems including multicut, multiway cut, and kcut, into a single problem. The input to the requirement cut problem is an undirected edgeweighted graph G = (V, E), and g groups of vertices X1, · · · , Xg ⊆ V, with each group Xi having a
Results 1  10
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88