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.
@article{arxiv.2211.12203,
title = {Edge Multiway Cut and Node Multiway Cut are NP-complete on subcubic graphs},
author = {Matthew Johnson and Barnaby Martin and Siani Smith and Sukanya Pandey and Daniel Paulusma and Erik Jan van Leeuwen},
journal= {arXiv preprint arXiv:2211.12203},
year = {2024}
}