[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 …

Fabrication of modified carbon nano tubes based composite using ionic liquid for phenol removal

N Rajamohan, S Bosu, GH Ngo, N Al-Shibli - Molecular Catalysis, 2022 - Elsevier
Carbon nano tubes are functionalized to enhance their surface properties and target
specificity. In this research, a novel ionic liquid functionalized carbon nanotube (IL-CNT) …

[HTML][HTML] Mim-width I. Induced path problems

L Jaffke, O Kwon, JA Telle - Discrete Applied Mathematics, 2020 - Elsevier
We initialize a series of papers deepening the understanding of algorithmic properties of the
width parameter maximum induced matching width (mim-width) of graphs. In this first volume …

Tree decompositions meet induced matchings: beyond Max Weight Independent Set

PT Lima, M Milanič, P Muršič, K Okrasa… - arXiv preprint arXiv …, 2024 - arxiv.org
For a tree decomposition $\mathcal {T} $ of a graph $ G $, by $\mu (\mathcal {T}) $ we
denote the size of a largest induced matching in $ G $ all of whose edges intersect one bag …

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 …

New width parameters for independent set: One-sided-mim-width and neighbor-depth

B Bergougnoux, T Korhonen, I Razgon - International Workshop on Graph …, 2023 - Springer
We study the tractability of the maximum independent set problem from the viewpoint of
graph width parameters, with the goal of defining a width parameter that is as general as …

[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 …

Comparing width parameters on graph classes

N Brettell, A Munaro, D Paulusma, S Yang - arXiv preprint arXiv …, 2023 - arxiv.org
We study how the relationship between non-equivalent width parameters changes once we
restrict to some special graph class. As width parameters, we consider treewidth, clique …

[HTML][HTML] On the thinness and proper thinness of a graph

F Bonomo, D de Estrada - Discrete Applied Mathematics, 2019 - Elsevier
Graphs with bounded thinness were defined in 2007 as a generalization of interval graphs.
In this paper we introduce the concept of proper thinness, such that graphs with bounded …

[HTML][HTML] On algorithmic applications of sim-width and mim-width of (H1, H2)-free graphs

A Munaro, S Yang - Theoretical Computer Science, 2023 - Elsevier
Mim-width and sim-width are among the most powerful graph width parameters, with sim-
width more powerful than mim-width, which is in turn more powerful than clique-width. While …