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Clique Partitions of Glued Graphs
"... A glued graph at K2clone (K3clone) results from combining two vertexdisjoint graphs by identifying an edge (a triangle) of each original graph. The clique covering numbers of these desired glued graphs have been investigated recently. Analogously, we obtain bounds of the clique partition numbers ..."
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A glued graph at K2clone (K3clone) results from combining two vertexdisjoint graphs by identifying an edge (a triangle) of each original graph. The clique covering numbers of these desired glued graphs have been investigated recently. Analogously, we obtain bounds of the clique partition numbers
The Facial Structure of the Clique Partitioning Polytope
, 1996
"... The clique partitioning problem (CPP) can be formulated as follows. Given is a complete graph G = (V; E), with edge weights w ij 2 R for all fi; jg 2 E. A subset A ` E is called a clique partition if there is a partition of V into nonempty, disjoint sets V 1 ; : : : ; V k , such that each V p (p = ..."
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Cited by 2 (1 self)
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The clique partitioning problem (CPP) can be formulated as follows. Given is a complete graph G = (V; E), with edge weights w ij 2 R for all fi; jg 2 E. A subset A ` E is called a clique partition if there is a partition of V into nonempty, disjoint sets V 1 ; : : : ; V k , such that each V p (p
ON THE FLY CLIQUE PARTITIONING FOR REGISTER ALLOCATION
"... In this endeavor a novel approach to a register allocation algorithm for Digital Synthesis is presented. Register allocation and functional unit allocation can reduce the overall cost of Application Specific Integrated Circuits (ASICS). Clique partitioning is one of the most efficient methods to ass ..."
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In this endeavor a novel approach to a register allocation algorithm for Digital Synthesis is presented. Register allocation and functional unit allocation can reduce the overall cost of Application Specific Integrated Circuits (ASICS). Clique partitioning is one of the most efficient methods
Dominator Colorings and Safe Clique Partitions
, 2006
"... Given a graph G, the dominator coloring problem seeks a proper coloring of G with the additional property that every vertex in the graph dominates an entire color class. The safe clique partition problem seeks a partition of the vertices of a graph into cliques with the additional property that for ..."
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Given a graph G, the dominator coloring problem seeks a proper coloring of G with the additional property that every vertex in the graph dominates an entire color class. The safe clique partition problem seeks a partition of the vertices of a graph into cliques with the additional property
On Intersection Representations and Clique Partitions of Graphs
, 2008
"... A multifamily set representation of a finite simple graph G is a multifamily F of sets (not necessarily distinct) for which each set represents a vertex in G and two sets in F intersects if and only if the two corresponding vertices are adjacent. For a graph G, an edge clique covering (edge clique p ..."
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partition, respectively) Q is a set of cliques for which every edge is contained in at least (exactly, respectively) one member of Q. In 1966, P. Erdös, A. Goodman, and L. Pósa (The representation of a graph by set intersections, Canadian J. Math., 18, pp.106112) pointed out that for a graph there is a one
Parameterized Complexity of the Clique Partition Problem
 In the fourteenth Computing: The Australasian Theory Symposium
, 2008
"... The problem of deciding whether the edgeset of a given graph can be partitioned into at most k cliques is well known to be NPcomplete. In this paper we investigate this problem from the point of view of parameterized complexity. We show that this problem is fixed parameter tractable if we choose t ..."
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Cited by 7 (2 self)
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The problem of deciding whether the edgeset of a given graph can be partitioned into at most k cliques is well known to be NPcomplete. In this paper we investigate this problem from the point of view of parameterized complexity. We show that this problem is fixed parameter tractable if we choose
Proving Facetness of Valid Inequalities for the Clique Partitioning Polytope
, 1996
"... In this paper we prove two lifting theorems for the clique partitioning problem. Each of these theorems implies that if a valid inequality satisfies certain conditions, then it de#nes a facet of the clique partitioning polytope. In particular if a valid inequality defines a facet of the polytope cor ..."
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Cited by 1 (0 self)
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In this paper we prove two lifting theorems for the clique partitioning problem. Each of these theorems implies that if a valid inequality satisfies certain conditions, then it de#nes a facet of the clique partitioning polytope. In particular if a valid inequality defines a facet of the polytope
An Efficient Algorithm for the Minimum Clique Partition Problem
, 2000
"... We design an algorithm for an exact solution of the Minimum Clique Partition Problem. For an arbitrary undirected graph G, we use a technique for finite partially ordered sets, in particular, a partition of such sets into the minimum number of paths. The running time of the algorithm is equal to O(n ..."
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We design an algorithm for an exact solution of the Minimum Clique Partition Problem. For an arbitrary undirected graph G, we use a technique for finite partially ordered sets, in particular, a partition of such sets into the minimum number of paths. The running time of the algorithm is equal to O
Results 1  10
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323