On algorithmic applications of sim-width and mim-width of (H 1,H 2)-free graphs

Andrea Munaro, Shizhou Yang

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
29 Downloads (Pure)

Abstract

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., A width parameter useful for chordal and co-comparability graphs, Theoretical Computer Science, 704:1-17, 2017], 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 , List k -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 Independent H -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 ( H 1 , H 2 ) -free graphs in the case H 1 is complete or edgeless. Our results solve some open problems in [Brettell et al., Bounding the mim-width of hereditary graph classes, Journal of Graph Theory, 99(1):117-151, 2022].
Original languageEnglish
Article number113825
Number of pages20
JournalTheoretical Computer Science
Volume955
Early online date20 Mar 2023
DOIs
Publication statusPublished - 26 Apr 2023

Fingerprint

Dive into the research topics of 'On algorithmic applications of sim-width and mim-width of (H 1,H 2)-free graphs'. Together they form a unique fingerprint.

Cite this