Maximum Cut on Interval Graphs of Interval Count Four is NP-Complete

Figueiredo, Celina M. H. de; Melo, Alexsander Andrade de; Oliveira, Fabiano S.; Silva, Ana

doi:10.1007/s00454-023-00508-x

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2023

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“…In this section, we present the notion of grained gadgets , which was defined in [6] as a generalization of the so‐called

V

‐ gadgets and

E

‐ gadgets . The latter was introduced by Adhikary et al [1] to prove the NP‐completeness of M ax C ut on interval graphs.…”

Section: Grained Gadgetmentioning

confidence: 99%

MaxCut on permutation graphs is NP‐complete

Figueiredo

Melo

Oliveira

et al. 2023

Journal of Graph Theory

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The decision problem MaxC ut is known to be NP‐complete since the seventies, but only recently its restriction to interval graphs has been announced to be hard by Adhikary, Bose, Mukherjee, and Roy. Building on their proof, in this paper we prove that the M axC ut problem is NP‐complete on permutation graphs. This settles a long‐standing open problem that appeared in the 1985 column of the Ongoing Guide to NP‐completeness by David S. Johnson, and is the first NP‐hardness entry for permutation graphs in such column.

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“…In this section, we present the notion of grained gadgets , which was defined in [6] as a generalization of the so‐called