[HTML][HTML] Cutting barnette graphs perfectly is hard
E Bonnet, D Chakraborty, J Duron - Theoretical Computer Science, 2024 - Elsevier
A perfect matching cut is a perfect matching that is also a cutset, or equivalently, a perfect
matching containing an even number of edges on every cycle. The corresponding …
matching containing an even number of edges on every cycle. The corresponding …
[HTML][HTML] Finding Matching Cuts in H-Free Graphs
F Lucke, D Paulusma, B Ries - Algorithmica, 2023 - Springer
The well-known NP-complete problem Matching Cut is to decide if a graph has a matching
that is also an edge cut of the graph. We prove new complexity results for Matching Cut …
that is also an edge cut of the graph. We prove new complexity results for Matching Cut …
Dichotomies for Maximum Matching Cut: -Freeness, Bounded Diameter, Bounded Radius
F Lucke, D Paulusma, B Ries - arXiv preprint arXiv:2304.01099, 2023 - arxiv.org
The (Perfect) Matching Cut problem is to decide if a graph $ G $ has a (perfect) matching cut,
ie, a (perfect) matching that is also an edge cut of $ G $. Both Matching Cut and Perfect …
ie, a (perfect) matching that is also an edge cut of $ G $. Both Matching Cut and Perfect …
Complexity results for matching cut problems in graphs without long induced paths
HO Le, VB Le - International Workshop on Graph-Theoretic Concepts …, 2023 - Springer
In a graph, a (perfect) matching cut is an edge cut that is a (perfect) matching. matching cut
(mc), respectively, perfect matching cut (pmc), is the problem of deciding whether a given …
(mc), respectively, perfect matching cut (pmc), is the problem of deciding whether a given …
[HTML][HTML] On the complexity of Matching Cut for graphs of bounded radius and H-free graphs
F Lucke, D Paulusma, B Ries - Theoretical Computer Science, 2022 - Elsevier
For a connected graph G=(V, E), a matching M⊆ E is a matching cut of G if G− M is
disconnected. It is known that for an integer d, the corresponding decision problem Matching …
disconnected. It is known that for an integer d, the corresponding decision problem Matching …
The perfect matching cut problem revisited
JA Telle - Theoretical Computer Science, 2022 - Elsevier
In a graph, a perfect matching cut is an edge cut that is a perfect matching. perfect matching
cut (pmc) is the problem of deciding whether a given graph has a perfect matching cut, and …
cut (pmc) is the problem of deciding whether a given graph has a perfect matching cut, and …
Matching cuts in graphs of high girth and H-free graphs
The (Perfect) Matching Cut problem is to decide if a connected graph has a (perfect)
matching that is also an edge cut. The Disconnected Perfect Matching problem is to decide if …
matching that is also an edge cut. The Disconnected Perfect Matching problem is to decide if …
A note on Matching-Cut in Pt-free graphs
C Feghali - Information Processing Letters, 2023 - Elsevier
A matching-cut of a graph is an edge cut that is a matching. The problem matching-cut is that
of recognizing graphs with a matching-cut and is NP-complete, even if the graph belongs to …
of recognizing graphs with a matching-cut and is NP-complete, even if the graph belongs to …
[HTML][HTML] On conflict-free cuts: Algorithms and complexity
J Rauch, D Rautenbach, US Souza - Information Processing Letters, 2025 - Elsevier
One way to define the Matching Cut problem is: Given a graph G, is there an edge-cut M of G
such that M is an independent set in the line graph of G? We propose the more general …
such that M is an independent set in the line graph of G? We propose the more general …
Polynomial-delay Enumeration Kernelizations for Cuts of Bounded Degree
L Kanesh, D Majumdar, MS Ramanujan - arXiv preprint arXiv:2308.01286, 2023 - arxiv.org
Enumeration kernelization was first proposed by Creignou et al.[TOCS 2017] and was later
refined by Golovach et al.[JCSS 2022] into two different variants: fully-polynomial …
refined by Golovach et al.[JCSS 2022] into two different variants: fully-polynomial …