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88
Quadrangularly connected claw-free graphs
"... A graph G is quadrangularly connected if for every pair of edges e1 and e2 in E(G), G has a sequence of l-cycles (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 claw-free 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 l-cycles (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 claw-free
Path extendability of claw-free graphs
, 2006
"... Let G be a connected, locally connected, claw-free graph of order n and x,y be two vertices of G. In this paper, we prove that if for any 2-cut 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, claw-free graph of order n and x,y be two vertices of G. In this paper, we prove that if for any 2-cut 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
Claw-free 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 claw-free graphs G with a clique the deletion of which disconnects G into two parts both with at least two vertices.
On stable cutsets in claw-free 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 NP-complete to decide whether a line graph (hence a claw-free graph) with maximum degree five or a K4-free 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 NP-complete to decide whether a line graph (hence a claw-free graph) with maximum degree five or a K4-free graph
Spanning Eulerian Subgraphs in claw-free graphs
"... A graph is claw-free if it has no induced K1,3 subgraph. A graph is essential 4-edge-connected if removing at most three edges, the resulting graph has at most one component having edges. In this note, we show that every essential 4-edgeconnected 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 claw-free if it has no induced K1,3 subgraph. A graph is essential 4-edge-connected if removing at most three edges, the resulting graph has at most one component having edges. In this note, we show that every essential 4-edgeconnected 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 2k2-partition
- 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 NP-complete. 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 NP-complete. 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
4-restricted edge cuts of graphs
- AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 30 (2004), PAGES 103–112
, 2004
"... A 4-restricted 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 4-restricted 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-restricte ..."
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A 4-restricted 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 4-restricted 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 k-cut, into a single problem. The input to the requirement cut problem is an undirected edge-weighted 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 k-cut, into a single problem. The input to the requirement cut problem is an undirected edge-weighted 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
