A logic-based algorithmic meta-theorem for mim-width

B Bergougnoux, J Dreier, L Jaffke - Proceedings of the 2023 Annual ACM …, 2023 - SIAM
We introduce a logic called distance neighborhood logic with acyclicity and connectivity
constraints (A&C DN for short) which extends existential MSO1 with predicates for querying …

[HTML][HTML] Treewidth versus clique number. III. Tree-independence number of graphs with a forbidden structure

C Dallard, M Milanič, K Štorgel - Journal of Combinatorial Theory, Series B, 2024 - Elsevier
We continue the study of (tw, ω)-bounded graph classes, that is, hereditary graph classes in
which the treewidth can only be large due to the presence of a large clique, with the goal of …

[HTML][HTML] Mim-width III. Graph powers and generalized distance domination problems

L Jaffke, O Kwon, TJF Strømme, JA Telle - Theoretical Computer Science, 2019 - Elsevier
We generalize the family of (σ, ρ) problems and locally checkable vertex partition problems
to their distance versions, which naturally captures well-known problems such as Distance-r …

Mim-width II. The feedback vertex set problem

L Jaffke, O Kwon, JA Telle - Algorithmica, 2020 - Springer
We give a first polynomial-time algorithm for (Weighted) Feedback Vertex Set on graphs of
bounded maximum induced matching width (mim-width). Explicitly, given a branch …

XNLP-completeness for parameterized problems on graphs with a linear structure

HL Bodlaender, C Groenland, H Jacob, L Jaffke… - Algorithmica, 2024 - Springer
In this paper, we showcase the class XNLP as a natural place for many hard problems
parameterized by linear width measures. This strengthens existing W [1]-hardness proofs for …

Bounding the mim‐width of hereditary graph classes

N Brettell, J Horsfield, A Munaro… - Journal of Graph …, 2022 - Wiley Online Library
A large number of NP‐hard graph problems are solvable in XP time when parameterized by
some width parameter. Hence, when solving problems on special graph classes, it is helpful …

[HTML][HTML] Treewidth versus clique number. II. Tree-independence number

C Dallard, M Milanič, K Štorgel - Journal of Combinatorial Theory, Series B, 2024 - Elsevier
In 2020, we initiated a systematic study of graph classes in which the treewidth can only be
large due to the presence of a large clique, which we call (tw, ω)-bounded. The family of (tw …

Node multiway cut and subset feedback vertex set on graphs of bounded mim-width

B Bergougnoux, C Papadopoulos, JA Telle - Algorithmica, 2022 - Springer
The two weighted graph problems Node Multiway Cut (NMC) and Subset Feedback Vertex
Set (SFVS) both ask for a vertex set of minimum total weight, that for NMC disconnects a …

Testing isomorphism of chordal graphs of bounded leafage is fixed-parameter tractable

V Arvind, R Nedela, I Ponomarenko… - International Workshop on …, 2022 - Springer
The computational complexity of the graph isomorphism problem is considered to be a
major open problem in theoretical computer science. It is known that testing isomorphism of …

On H-Topological Intersection Graphs

S Chaplick, M Töpfer, J Voborník, P Zeman - Graph-Theoretic Concepts in …, 2017 - Springer
Abstract Biró, Hujter, and Tuza introduced the concept of H-graphs (1992), intersection
graphs of connected subgraphs of a subdivision of a graph H. They naturally generalize …