Graphs & digraphs (2nd ed.)
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Invitation to data reduction and problem kernelization
ACM SIGACT News
Data reduction and exact algorithms for clique cover
Journal of Experimental Algorithmics (JEA)
Efficient parameterized preprocessing for cluster editing
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
Parameterized Complexity
Covering graphs with few complete bipartite subgraphs
Theoretical Computer Science
CGGA'10 Proceedings of the 9th international conference on Computational Geometry, Graphs and Applications
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The problem of deciding whether the edge-set of a given graph can be partitioned into at most k cliques is well known to be NP-complete. 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 the number of cliques as parameter. In particular, we show that in polynomial time, a kernel bounded by k2 can be obtained, where k is the number of cliques. We also give an O(2((k+3) log k)/2n) algorithm for this problem in K4-free graphs.