Edge Multiway Cut and Node Multiway Cut are NP-complete on subcubic graphs

Matthew Johnson; Barnaby Martin; Siani Smith; Sukanya Pandey; Daniel Paulusma; Erik Jan van Leeuwen

doi:10.4230/lipics.swat.2024.29

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arXiv · 2211.12203

Edge Multiway Cut and Node Multiway Cut are NP-complete on subcubic graphs

Matthew Johnson·Barnaby Martin·Siani Smith·Sukanya Pandey·Daniel Paulusma·Erik Jan van Leeuwen

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Abstract

We show that Edge Multiway Cut (also called Multiterminal Cut) and Node Multiway Cut are NP-complete on graphs of maximum degree $3$ (also known as subcubic graphs). This improves on a previous degree bound of $11$. Our NP-completeness result holds even for subcubic graphs that are planar.

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Matthew Johnson, Barnaby Martin, Siani Smith, Sukanya Pandey, Daniel Paulusma, Erik Jan van Leeuwen. 2022-11-22. Edge Multiway Cut and Node Multiway Cut are NP-complete on subcubic graphs. https://doi.org/10.4230/lipics.swat.2024.29

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