# Parameterized Algorithms for Maximum Cut with Connectivity Constraints

arXiv: https://arxiv.org/abs/1908.03389 · HTML: https://mlsanity.com/paper/1908.03389/

## Key facts

- Cited by 1 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 9 Aug 2019.

## Built on by (most cited first, 1 of 1)

- [An Unsupervised Learning Framework Combined with Heuristics for the Maximum Minimal Cut Problem](https://mlsanity.com/paper/2408.08484/) (2024)

## Abstract (arXiv)

We study two variants of textscMaximum Cut, which we call textscConnected Maximum Cut and textscMaximum Minimal Cut, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some connectivity requirements. Both problems are known to be NP-complete even on planar graphs whereas textscMaximum Cut on planar graphs is solvable in polynomial time. We first show that these problems are NP-complete even on planar bipartite graphs and split graphs. Then we give parameterized algorithms using graph parameters such as clique-width, tree-width, and twin-cover number. Finally, we obtain FPT algorithms with respect to the solution size.