On algorithmic applications of sim-width and mim-width of (H1,H2)-free graphs

Mim-width and sim-width are among the most powerful graph width parameters, with sim-width more powerful than mim-width, which is in turn more powerful than clique-width. While several NP-hard graph problems become tractable for graph classes whose mim-width is bounded and quickly computable, no alg...

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Veröffentlicht in:Theoretical computer science Jg. 955; S. 113825
Hauptverfasser: Munaro, Andrea, Yang, Shizhou
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 26.04.2023
Schlagworte:
[formula omitted] algorithm
Hereditary graph class
Mim-width
Sim-width
Width parameter
XP algorithm
Mim-width
Sim-width
Hereditary graph class
Width parameter
ISSN:0304-3975
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Zusammenfassung:Mim-width and sim-width are among the most powerful graph width parameters, with sim-width more powerful than mim-width, which is in turn more powerful than clique-width. While several NP-hard graph problems become tractable for graph classes whose mim-width is bounded and quickly computable, no algorithmic applications of boundedness of sim-width are known. In Kang et al. (2017) [32], it is asked whether Independent Set and 3-Colouring are NP-complete on graphs of sim-width at most 1. We observe that, for each k∈N, Listk-Colouring is polynomial-time solvable for graph classes whose sim-width is bounded and quickly computable. Moreover, we show that if the same holds for Independent Set, then IndependentH-Packing is polynomial-time solvable for graph classes whose sim-width is bounded and quickly computable. This problem is a common generalisation of Independent Set, Induced Matching, Dissociation Set and k-Separator. We also make progress toward classifying the mim-width of (H1,H2)-free graphs in the case H1 is complete or edgeless. Our results solve some open problems in Brettell et al. (2022) [6].
ISSN:0304-3975
DOI:10.1016/j.tcs.2023.113825