Abstract
Weighted independent domination is an NP-hard graph problem, which remains computationally intractable in many restricted graph classes. Only few examples of classes are available, where the problem admits polynomial-time solutions. In the present paper, we extend the short list of such classes with two new examples.
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Balas, E., Yu, C.S.: On graphs with polynomially solvable maximum-weight clique problem. Networks 19, 247–253 (1989)
Bodlaender, H.L., Brandstädt, A., Kratsch, D., Rao, M., Spinrad, J.: On algorithms for \((P_5, gem)\)-free graphs. Theoret. Comput. Sci. 349, 2–21 (2005)
Boliac, R., Lozin, V.: Independent domination in finitely defined classes of graphs. Theoret. Comput. Sci. 301, 271–284 (2003)
Chang, G.J.: The weighted independent domination problem is NP-complete for chordal graphs. Discret. Appl. Math. 143, 351–352 (2004)
Damaschke, P., Muller, H., Kratsch, D.: Domination in convex and chordal bipartite graphs. Inf. Process. Lett. 36, 231–236 (1990)
Farber, M.: Independent domination in chordal graphs. Oper. Res. Lett. 1, 134–138 (1982)
Giakoumakis, V., Rusu, I.: Weighted parameters in \((P_5,\overline{P}_5)\)-free graphs. Discret. Appl. Math. 80, 255–261 (1997)
Karthick, T.: On atomic structure of \(P_5\)-free subclasses and maximum weight independent set problem. Theoret. Comput. Sci. 516, 78–85 (2014)
Lokshantov, D., Vatshelle, M., Villanger, Y.: Independent set in \(P_5\)-free graphs in polynomial time. In: Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 570–581 (2014)
Lozin, V., Mosca, R., Purcell, C.: Independent domination in finitely defined classes of graphs: polynomial algorithms. Discret. Appl. Math. 182, 2–14 (2015)
McConnell, R.M., Spinrad, J.: Modular decomposition and transitive orientation. Discret. Math. 201, 189–241 (1999)
Möhring, R.H., Radermacher, F.J.: Substitution decomposition for discrete structures and connections with combinatorial optimization. Ann. Discret. Math. 19, 257–356 (1984)
Whitesides, S.H.: An algorithm for finding clique cut-sets. Inf. Process. Lett. 12, 31–32 (1981)
Yannakakis, M., Gavril, F.: Edge dominating sets in graphs. SIAM J. Appl. Math. 38, 364–372 (1980)
Zverovich, I.E.: Satgraphs and independent domination. Part 1. Theoret. Comput. Sci. 352, 47–56 (2006)
Acknowledgements
The results of Sect. 3 were obtained under financial support of the Russian Science Foundation grant No. 17-11-01336. The results of Sect. 4 were obtained under financial support of the Russian Foundation for Basic Research, grant No. 16-31-60008-mol-a-dk, RF President grant MK-4819.2016.1 and LATNA laboratory, National Research University Higher School of Economics.
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Lozin, V., Malyshev, D., Mosca, R., Zamaraev, V. (2017). New Results on Weighted Independent Domination. In: Bodlaender, H., Woeginger, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 2017. Lecture Notes in Computer Science(), vol 10520. Springer, Cham. https://doi.org/10.1007/978-3-319-68705-6_30
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DOI: https://doi.org/10.1007/978-3-319-68705-6_30
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