Related papers: Parameterized Complexity of the Star Decomposition…
A graph $H$ is {\em $p$-edge colorable} if there is a coloring $\psi: E(H) \rightarrow \{1,2,\dots,p\}$, such that for distinct $uv, vw \in E(H)$, we have $\psi(uv) \neq \psi(vw)$. The {\sc Maximum Edge-Colorable Subgraph} problem takes as…
The K-way vertex cut problem} consists in, given a graph G, finding a subset of vertices of a given size, whose removal partitions G into the maximum number of connected components. This problem has many applications in several areas. It…
The problem of deciding whether a biconnected planar digraph $G=(V,E)$ can be augmented to become an $st$-planar graph by adding a set of oriented edges $E' \subseteq V \times V$ is known to be NP-complete. We show that the problem is…
Given a graph $G = (V,E)$, $A \subseteq V$, and integers $k$ and $\ell$, the \textsc{$(A,\ell)$-Path Packing} problem asks to find $k$ vertex-disjoint paths of length $\ell$ that have endpoints in $A$ and internal points in $V \setminus A$.…
We study the linear extension complexity of stable set polytopes of perfect graphs. We make use of known structural results permitting to decompose perfect graphs into basic perfect graphs by means of two graph operations: 2-join and skew…
Given a straight-line drawing of a graph, a segment is a maximal set of edges that form a line segment. Given a planar graph $G$, the segment number of $G$ is the minimum number of segments that can be achieved by any planar straight-line…
An $(r, \ell)$-partition of a graph $G$ is a partition of its vertex set into $r$ independent sets and $\ell$ cliques. A graph is $(r, \ell)$ if it admits an $(r, \ell)$-partition. A graph is well-covered if every maximal independent set is…
We investigate the parameterized complexity of several problems formalizing cluster identification in graphs. In other words we ask whether a graph contains a large enough and sufficiently connected subgraph. We study here three relaxations…
We consider the following problem: for a given graph $G$ and two integers $k$ and $d$, can we apply a fixed graph operation at most $k$ times in order to reduce a given graph parameter $\pi$ by at least $d$? We show that this problem is…
Given a graph $G$ and a parameter $k$, the $k$-biclique problem asks whether $G$ contains a complete bipartite subgraph $K_{k,k}$. This is the most easily stated problem on graphs whose parameterized complexity is still unknown. We provide…
We study edge-decompositions of highly connected graphs into copies of a given tree. In particular we attack the following conjecture by Bar\'at and Thomassen: for each tree $T$, there exists a natural number $k_T$ such that if $G$ is a…
Given a graph $G$ and a positive integer $k$, the 2-Load coloring problem is to check whether there is a $2$-coloring $f:V(G) \rightarrow \{r,b\}$ of $G$ such that for every $i \in \{r,b\}$, there are at least $k$ edges with both end…
We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…
Bhawalkar, Kleinberg, Lewi, Roughgarden, and Sharma [ICALP 2012] introduced the Anchored k-Core problem, where the task is for a given graph G and integers b, k, and p to find an induced subgraph H with at least p vertices (the core) such…
We introduce the Multicolored Graph Realization problem (MGRP). The input to the problem is a colored graph $(G,\varphi)$, i.e., a graph together with a coloring on its vertices. We can associate to each colored graph a cluster graph…
We study the SHORTEST PATH problem with positive disjunctive constraints from the perspective of parameterized complexity. For positive disjunctive constraints, there are certain pair of edges such that any feasible solution must contain at…
Given a simple connected undirected graph G = (V, E), a set X \subseteq V(G), and integers k and p, STEINER SUBGRAPH EXTENSION problem asks if there exists a set S \supseteq X with at most k vertices such that G[S] is p-edge-connected. This…
A decomposition of a multigraph $G$ is a partition of its edges into subgraphs $G(1), \ldots , G(k)$. It is called an $r$-factorization if every $G(i)$ is $r$-regular and spanning. If $G$ is a subgraph of $H$, a decomposition of $G$ is said…
For two integers $r, \ell \geq 0$, a graph $G = (V, E)$ is an $(r,\ell)$-graph if $V$ can be partitioned into $r$ independent sets and $\ell$ cliques. In the parameterized $(r,\ell)$-Vertex Deletion problem, given a graph $G$ and an integer…
An $\ell$-page stack layout (also known as an $\ell$-page book embedding) of a graph is a linear order of the vertex set together with a partition of the edge set into $\ell$ stacks (or pages), such that the endpoints of no two edges on the…