Abstract
The linear maximum induced matching width (LMIM-width) of a graph is a width parameter based on the maximum induced matching in some of its subgraphs. In this paper we study output-polynomial enumeration algorithms on graphs of bounded LMIM-width and graphs of bounded local LMIM-width. In particular, we show that all 1-minimal \((\sigma ,\rho )\)-dominating sets, and hence all minimal dominating sets, of graphs of bounded LMIM-width can be enumerated with polynomial (linear) delay using polynomial space. Furthermore, we show that all minimal dominating sets of a unit square graph can be enumerated in incremental polynomial time.
The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n. 267959.
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Golovach, P.A., Heggernes, P., Kanté, M.M., Kratsch, D., Sæther, S.H., Villanger, Y. (2015). Output-Polynomial Enumeration on Graphs of Bounded (Local) Linear MIM-Width. In: Elbassioni, K., Makino, K. (eds) Algorithms and Computation. ISAAC 2015. Lecture Notes in Computer Science(), vol 9472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48971-0_22
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