Various properties of various ultrafilters, various graph width parameters, and various connectivity systems (with survey)

T Fujita - arxiv preprint arxiv:2408.02299, 2024 - arxiv.org
This paper investigates ultrafilters in the context of connectivity systems, defined as pairs
$(X, f) $ where $ X $ is a finite set and $ f $ is a symmetric submodular function. Ultrafilters …

Width parameters beyond tree-width and their applications

P Hliněný, S Oum, D Seese, G Gottlob - The computer journal, 2008 - ieeexplore.ieee.org
Besides the very successful concept of tree-width (see [Bodlaender, H. and Koster, A.(2007)
Combinatorial optimisation on graphs of bounded treewidth. These are special issues on …

Clique-width is NP-complete

MR Fellows, FA Rosamond, U Rotics, S Szeider - SIAM Journal on Discrete …, 2009 - SIAM
Clique-width is a graph parameter that measures in a certain sense the complexity of a
graph. Hard graph problems (eg, problems expressible in monadic second-order logic with …

Clique-width for hereditary graph classes.

KK Dabrowski, M Johnson, D Paulusma - BCC, 2019 - books.google.com
Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic
tractability: if the clique-width of a graph class G is bounded by a constant, a wide range of …

[HTML][HTML] Classes of graphs with low complexity: The case of classes with bounded linear rankwidth

J Nešetřil, PO de Mendez, R Rabinovich… - European Journal of …, 2021 - Elsevier
Classes with bounded rankwidth are MSO-transductions of trees and classes with bounded
linear rankwidth are MSO-transductions of paths–a result that shows a strong link between …

The behavior of clique-width under graph operations and graph transformations

F Gurski - Theory of Computing Systems, 2017 - Springer
Clique-width is a well-known graph parameter. Many NP-hard graph problems admit
polynomial-time solutions when restricted to graphs of bounded clique-width. The same …

Clique-width minimization is NP-hard

MR Fellows, FA Rosamond, U Rotics… - Proceedings of the thirty …, 2006 - dl.acm.org
Clique-width is a graph parameter that measures in a certain sense the complexity of a
graph. Hard graph problems (eg, problems expressible in Monadic Second Order Logic with …

A SAT approach to clique-width

MJH Heule, S Szeider - ACM Transactions on Computational Logic …, 2015 - dl.acm.org
Clique-width is a graph invariant that has been widely studied in combinatorics and
computational logic. Computing the clique-width of a graph is an intricate problem, because …

Tight Algorithm for Connected Odd Cycle Transversal Parameterized by Clique-width

N Bojikian, S Kratsch - arxiv preprint arxiv:2402.08046, 2024 - arxiv.org
Recently, Bojikian and Kratsch [2023] have presented a novel approach to tackle
connectivity problems parameterized by clique-width ($\operatorname {cw} $), based on …

Comparing linear width parameters for directed graphs

F Gurski, C Rehs - Theory of Computing Systems, 2019 - Springer
In this paper we introduce the linear clique-width, linear NLC-width, neighbourhood-width,
and linear rank-width for directed graphs. We compare these parameters with each other as …