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Combinatorics, Probability and Computing, 1996
In this paper, we prove that every graph contains a cycle intersecting all maximum independent sets. Using this, we further prove that every graph with stability number α is spanned by α disjoint cycles. Here, the empty set, the graph of order 1 and the path of order 2 are all considered as degenerate cycles.
Chen, C.C., Jin, G.P.
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In this paper, we prove that every graph contains a cycle intersecting all maximum independent sets. Using this, we further prove that every graph with stability number α is spanned by α disjoint cycles. Here, the empty set, the graph of order 1 and the path of order 2 are all considered as degenerate cycles.
Chen, C.C., Jin, G.P.
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A graph partition problem [PDF]
Acta Mathematicae Applicatae Sinica, 1996 Let \(G= (V,E)\) be a graph, and \(e_1\), \(e_2\) disjoint edges of \(G\). Suppose that \(E-\{e_1,e_2\}\) can be partitioned into sets \(E_1\) and \(E_2\), where \(G_i\) is the subgraph spanned by \(E_i\), \(i=1,2\). Also suppose that \(G_1\) has each of its components unicyclic and \(G_2\) has exactly four components that are trees, each one incident ...
Simeone Bruno +2 more
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Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures, 2004
In this paper we consider the problem of (k, υ)-balanced graph partitioning - dividing the vertices of a graph into k almost equal size components (each of size less than υ • nk) so that the capacity of edges between different components is minimized. This problem is a natural generalization of several other problems such as minimum bisection, which is
Harald Räcke, Konstantin Andreev
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In this paper we consider the problem of (k, υ)-balanced graph partitioning - dividing the vertices of a graph into k almost equal size components (each of size less than υ • nk) so that the capacity of edges between different components is minimized. This problem is a natural generalization of several other problems such as minimum bisection, which is
Harald Räcke, Konstantin Andreev
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Mathematical Methods of Operations Research (ZOR), 2002
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William W. Hager, Yaroslav Krylyuk
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
William W. Hager, Yaroslav Krylyuk
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Journal of Graph Theory, 1997
Packing by induced stars is characterised.
Yoshimi Egawa +2 more
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Packing by induced stars is characterised.
Yoshimi Egawa +2 more
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The partition dimension of a graph
Aequationes Mathematicae, 2000An ordered partition of the vertices of a graph \(G\) is resolving if all vertices have distinct vectors of distances to the partition classes. The partition dimension pd\((G)\) of \(G\) is the smallest size of a resolving partition. This turns out to be at most 1 more than the metric dimension, obtained similarly, after substituting partitions by ...
Ebrahim Salehi +2 more
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SIAM Journal on Computing, 1992
The graph partitioning problem is the problem of dividing a given graph of \(n\) nodes into two sets of prescribed size while cutting a minimum number of edges. The authors show that the partitioning problem of a planar graph can be solved in polynomial time if the cutsize of the optimal partition is \(O(\log n)\) or if an embedding of the graph is ...
Thang Nguyen Bui, Andrew Wynne Peck
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The graph partitioning problem is the problem of dividing a given graph of \(n\) nodes into two sets of prescribed size while cutting a minimum number of edges. The authors show that the partitioning problem of a planar graph can be solved in polynomial time if the cutsize of the optimal partition is \(O(\log n)\) or if an embedding of the graph is ...
Thang Nguyen Bui, Andrew Wynne Peck
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The Optimal Partitioning of Graphs
SIAM Journal on Applied Mathematics, 1976The problem considered in this paper is that of partitioning a link-weighted graph G into two parts, each of which is constrained in size by the (given) maximum number of vertices that the part can contain. This is a special case of the general partitioning problem of a graph into k parts with size constraints, which appears in a number of very diverse
Nicos Christofides, P. Brooker
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