Filters are collections of sets that are closed under supersets and finite intersections, serving
as fundamental tools in topology and set theory. An ultrafilter, a maximal filter on a set, plays …

Recently, hardness results for problems in P were achieved using reasonable complexity-
theoretic assumptions such as the Strong Exponential Time Hypothesis. According to these …

Many fundamental NP NP-hard problems can be formulated as integer linear programs
(ILPs). A famous algorithm by Lenstra solves ILPs in time that is exponential only in the …

We revisit the complexity of the classical k-Coloring problem parameterized by clique-width.
This is a very well-studied problem that becomes highly intractable when the number of …

Powerful results from the theory of integer programming have recently led to substantial
advances in parameterized complexity. However, our perception is that, except for Lenstra's …

Structural graph parameters, such as treewidth, pathwidth, and clique-width, are a central
topic of study in parameterized complexity. A main aim of research in this area is to …

An enumeration kernel as defined by Creignou et al.(2017)[11] for a parameterized
enumeration problem consists of an algorithm that transforms each instance into one whose …

The notion of resolving sets in a graph was introduced by Slater Proceedings of the Sixth
Southeastern Conference on Combinatorics, Graph Theory, and Computing, Util. Math …

Parameterized complexity seeks to use input structure to obtain faster algorithms for NP-
hard problems. This has been most successful for graphs of low treewidth: Many problems …

Graph Burning asks, given a graph G=(V, E) and an integer k, whether there exists (b 0,⋯, bk-
1)∈ V k such that every vertex in G has distance at most i from some bi. This problem is …