Geodesic
Application of the clique minimal separator decomposition to finding the maximum weight $\{K_1,K_2,k,l\}$-packing in a graph
Trudy Instituta matematiki, Tome 30 (2022) no. 1, pp. 44-49

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The maximum weight $(\{ K_{1} ,K_{2} \} ,k,l)$-packing problem in graph is considered. This problem generalizes a number of well-known problems, for example: maximum induced matching, k-separated matching, connected matching, independent set, dissociating set, $k$-packing. Let $\Gamma $ be a class of graphs and $\Gamma^*$ the class of all atoms (with respect to the clique minimal separator decomposition) generated subgraphs from $\Gamma $. Proof that if the maximum weight $(\{ K_{1} ,K_{2} \} ,k,l)$-packing problem can be solve in the class of graphs $\Gamma^*$ in time $O(f_{atoms}(n)),$ then this problem can be solved in the class of graphs $\Gamma$ in time $O(n(n+m)\cdot f_{atoms}(n)).$ 
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V. V. Lepin. Application of the clique minimal separator decomposition to finding the maximum weight $\{K_1,K_2,k,l\}$-packing in a graph. Trudy Instituta matematiki, Tome 30 (2022) no. 1, pp. 44-49. http://geodesic.mathdoc.fr/item/TIMB_2022_30_1_a5/