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 …
$(X, f) $ where $ X $ is a finite set and $ f $ is a symmetric submodular function. Ultrafilters …
Width parameters beyond tree-width and their applications
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 …
Combinatorial optimisation on graphs of bounded treewidth. These are special issues on …
Clique-width is NP-complete
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 …
graph. Hard graph problems (eg, problems expressible in monadic second-order logic with …
Clique-width for hereditary graph classes.
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 …
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
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 …
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 …
polynomial-time solutions when restricted to graphs of bounded clique-width. The same …
Clique-width minimization is NP-hard
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 …
graph. Hard graph problems (eg, problems expressible in Monadic Second Order Logic with …
A SAT approach to clique-width
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 …
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
Recently, Bojikian and Kratsch [2023] have presented a novel approach to tackle
connectivity problems parameterized by clique-width ($\operatorname {cw} $), based on …
connectivity problems parameterized by clique-width ($\operatorname {cw} $), based on …
Comparing linear width parameters for directed graphs
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 …
and linear rank-width for directed graphs. We compare these parameters with each other as …