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INTRINSIC KNOTTING OF PARTITE GRAPHS
"... Abstract. We introduce theorems that identify partite graphs that are intrinsically knotted (IK) since they contain subgraphs that are intrinsically knotted. We show that if we increase the number of vertices in each of the parts except one and delete an edge of an intrinsically knotted graph of tw ..."
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Abstract. We introduce theorems that identify partite graphs that are intrinsically knotted (IK) since they contain subgraphs that are intrinsically knotted. We show that if we increase the number of vertices in each of the parts except one and delete an edge of an intrinsically knotted graph
ON INTEGRAL COMPLETE R−PARTITE GRAPHS
"... AgraphG is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper we investigate integral complete r−partite graphs Kp1,p2,...,pr = Ka1p1,a2p2,...,asps with s ≤ 4. New sufficient conditions for complete 3partite graphs and complete 4partite graphs to be integral ..."
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AgraphG is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper we investigate integral complete r−partite graphs Kp1,p2,...,pr = Ka1p1,a2p2,...,asps with s ≤ 4. New sufficient conditions for complete 3partite graphs and complete 4partite graphs
Unsupervised Learning on Kpartite Graphs
, 2006
"... Various data mining applications involve data objects of multiple types that are related to each other, which can be naturally formulated as a kpartite graph. However, the research on mining the hidden structures from a kpartite graph is still limited and preliminary. In this paper, we propose a g ..."
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Cited by 46 (4 self)
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Various data mining applications involve data objects of multiple types that are related to each other, which can be naturally formulated as a kpartite graph. However, the research on mining the hidden structures from a kpartite graph is still limited and preliminary. In this paper, we propose a
INTRINSIC LINKING OF COMPLETE PARTITE GRAPHS
, 2003
"... Abstract. We classify complete partite graphs with respect to intrinsic linking. In Adams’s The Knot Book, it is conjectured that on removing a vertex from an intrinsically knotted graph, one obtains an intrinsically linked graph. We verify this conjecture for the class of complete partite graphs. 1 ..."
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Abstract. We classify complete partite graphs with respect to intrinsic linking. In Adams’s The Knot Book, it is conjectured that on removing a vertex from an intrinsically knotted graph, one obtains an intrinsically linked graph. We verify this conjecture for the class of complete partite graphs
Partitioning Graphs into Balanced Components
, 2009
"... We consider the kbalanced partitioning problem, where the goal is to partition the vertices of an input graph G into k equally sized components, while minimizing the total weight of the edges connecting different components. We allow k to be part of the input and denote the cardinality of the verte ..."
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Cited by 18 (2 self)
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We consider the kbalanced partitioning problem, where the goal is to partition the vertices of an input graph G into k equally sized components, while minimizing the total weight of the edges connecting different components. We allow k to be part of the input and denote the cardinality
On Decomposing 4partite Graphs Into Triangles
, 1993
"... We prove that for a 4partite graph of order n with b n 2 4 c + k edges, there exists an edgedisjoint collection of at least k \Gamma O(n) triangles. ..."
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We prove that for a 4partite graph of order n with b n 2 4 c + k edges, there exists an edgedisjoint collection of at least k \Gamma O(n) triangles.
Domination in Partitioned Graphs
"... Let V 1 ; V 2 be a partition of the vertex set in a graph G, let denote the domination number of G and let i denote the least number of vertices needed in G to dominate V i . We prove that 1 + 2 4 5 jV (G)j for any graph without isolated vertices or edges, and that equality occurs precisely if G con ..."
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Cited by 4 (3 self)
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Let V 1 ; V 2 be a partition of the vertex set in a graph G, let denote the domination number of G and let i denote the least number of vertices needed in G to dominate V i . We prove that 1 + 2 4 5 jV (G)j for any graph without isolated vertices or edges, and that equality occurs precisely if G
Partitioning Graphs of Regular Degree
"... GraphPartitioning problems occur in a wide range of applications. The task is to divide the vertices of a graph in equally sized parts such that as few edges as possible are crossing the boundaries. The calculation of an optimal result is NPcomplete. We show a new strategy to derive upper bounds o ..."
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GraphPartitioning problems occur in a wide range of applications. The task is to divide the vertices of a graph in equally sized parts such that as few edges as possible are crossing the boundaries. The calculation of an optimal result is NPcomplete. We show a new strategy to derive upper bounds
Results 1  10
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315,164