Related papers: Parameterized Pre-coloring Extension and List Colo…
Given a directed graph $D$ on $n$ vertices and a positive integer $k$, the Arc-Disjoint Cycle Packing problem is to determine whether $D$ has $k$ arc-disjoint cycles. This problem is known to be W[1]-hard in general directed graphs. In this…
For a fixed integer, the $k$-Colouring problem is to decide if the vertices of a graph can be coloured with at most $k$ colours for an integer $k$, such that no two adjacent vertices are coloured alike. A graph $G$ is $H$-free if $G$ does…
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 colors $k$ is large. However, much less is known on its…
In the NP-hard Edge Dominating Set problem (EDS) we are given a graph $G=(V,E)$ and an integer $k$, and need to determine whether there is a set $F\subseteq E$ of at most $k$ edges that are incident with all (other) edges of $G$. It is…
Let $F$ be a (possibly improper) edge-coloring of a graph $G$; a vertex coloring of $G$ is \emph{adapted to} $F$ if no color appears at the same time on an edge and on its two endpoints. If for some integer $k$, a graph $G$ is such that…
We investigate polynomial-time preprocessing for the problem of hitting forbidden minors in a graph, using the framework of kernelization. For a fixed finite set of connected graphs F, the F-Deletion problem is the following: given a graph…
A graph is geometric 1-planar if it admits a straight-line drawing where each edge is crossed at most once. We provide the first systematic study of the parameterized complexity of recognizing geometric 1-planar graphs. By substantially…
A decision problem is called parameterized if its input is a pair of strings. One of these strings is referred to as a parameter. The problem: given a propositional logic program P and a non-negative integer k, decide whether P has a stable…
A parameterized problem consists of a classical problem and an additional component, the so-called parameter. This point of view allows a formal definition of preprocessing: Given a parameterized instance (I,k), a polynomial kernelization…
A packing $k$-coloring for some integer $k$ of a graph $G=(V,E)$ is a mapping $\varphi:V\to\{1,\ldots,k\}$ such that any two vertices $u, v$ of color $\varphi(u)=\varphi(v)$ are in distance at least $\varphi(u)+1$. This concept is motivated…
We provide a polynomial-time algorithm for b-Coloring on graphs of constant clique-width. This unifies and extends nearly all previously known polynomial time results on graph classes, and answers open questions posed by Campos and Silva…
Given a graph G, a q-open neighborhood conflict-free coloring or q-ONCF-coloring is a vertex coloring $c:V(G) \rightarrow \{1,2,\ldots,q\}$ such that for each vertex $v \in V(G)$ there is a vertex in $N(v)$ that is uniquely colored from the…
We continue the study initiated by Bonomo-Braberman and Gonzalez in 2020 on $r$-locally checkable problems. We propose a dynamic programming algorithm that takes as input a graph with an associated clique-width expression and solves a…
We present randomized algorithms for some well-studied, hard combinatorial problems: the k-path problem, the p-packing of q-sets problem, and the q-dimensional p-matching problem. Our algorithms solve these problems with high probability in…
For graph classes $P_1,...,P_k$, Generalized Graph Coloring is the problem of deciding whether the vertex set of a given graph $G$ can be partitioned into subsets $V_1,...,V_k$ so that $V_j$ induces a graph in the class $P_j$…
In the Proper Interval Vertex Deletion problem (PIVD for short), we are given a graph $G$ and an integer parameter $k>0$, and the question is whether there are at most $k$ vertices in $G$ whose removal results in a proper interval graph. It…
We present new randomized algorithms that improve the complexity of the classic $(\Delta+1)$-coloring problem, and its generalization $(\Delta+1)$-list-coloring, in three well-studied models of distributed, parallel, and centralized…
In this paper we study the complexity of the following problems: Given a colored graph X=(V,E,c), compute a minimum cardinality set S of vertices such that no nontrivial automorphism of X fixes all vertices in S. A closely related problem…
In this paper, we devise a scheme for kernelizing, in sublinear space and polynomial time, various problems on planar graphs. The scheme exploits planarity to ensure that the resulting algorithms run in polynomial time and use O((sqrt(n) +…
The Rainbow k-Coloring problem asks whether the edges of a given graph can be colored in $k$ colors so that every pair of vertices is connected by a rainbow path, i.e., a path with all edges of different colors. Our main result states that…