Related papers: The Parameterized Complexity of Fixing Number and …
An assignment of colours to the vertices of a graph is stable if any two vertices of the same colour have identically coloured neighbourhoods. The goal of colour refinement is to find a stable colouring that uses a minimum number of…
The paper considers the NP-hard graph vertex coloring problem, which differs from traditional problems in which it is required to color vertices with a given (or minimal) number of colors so that adjacent vertices have different colors. In…
This work studies the parameterized complexity of finding secluded solutions to classical combinatorial optimization problems on graphs such as finding minimum s-t separators, feedback vertex sets, dominating sets, maximum independent sets,…
We study the algorithmic complexity of partitioning the vertex set of a given (di)graph into a small number of paths. The Path Partition problem (PP) has been studied extensively, as it includes Hamiltonian Path as a special case. The…
Given a bipartite graph $G=(U\cup V,E)$, a left-perfect many-to-one matching is a subset $M \subseteq E$ such that each vertex in $U$ is incident with exactly one edge in $M$. If $U$ is partitioned into some groups, the matching is called…
Let $G$ be a graph on $n$ vertices and $\mathrm{STAB}_k(G)$ be the convex hull of characteristic vectors of its independent sets of size at most $k$. We study extension complexity of $\mathrm{STAB}_k(G)$ with respect to a fixed parameter…
In this work, we study the problem of computing a maximum common contraction of two vertex-labeled graphs, i.e. how to make them identical by contracting as little edges as possible in the two graphs. We study the problem from a…
We consider the parameterised complexity of several list problems on graphs, with parameter treewidth or pathwidth. In particular, we show that List Edge Chromatic Number and List Total Chromatic Number are fixed parameter tractable,…
We study the Induced $H$ Partition problem from the parameterized complexity point of view. In the Induced $H$ Partition problem the task is to partition vertices of a graph $G$ into sets $V_1,V_2,\dots,V_n$ such that the graph $H$ is…
We study the parameterized complexity of the graph isomorphism problem when parameterized by width parameters related to tree decompositions. We apply the following technique to obtain fixed-parameter tractability for such parameters. We…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
Graph coloring problems are a central topic of study in the theory of algorithms. We study the problem of partially coloring partially colorable graphs. For $\alpha \leq 1$ and $k \in \mathbb{Z}^+$, we say that a graph $G=(V,E)$ is…
Subgraph Isomorphism is a very basic graph problem, where given two graphs $G$ and $H$ one is to check whether $G$ is a subgraph of $H$. Despite its simple definition, the Subgraph Isomorphism problem turns out to be very broad, as it…
We study the well-established problem of finding an optimal routing of unsplittable flows in a graph. While by now there is an extensive body of work targeting the problem on graph classes such as paths and trees, we aim at using the…
The graph isomorphism (GI) problem, which asks whether two graphs are structurally identical, occupies a unique position in computational complexity -- it is neither known to be solvable in polynomial time, nor proven to be NP-complete. We…
Given $k$ input graphs $G_1, \dots ,G_k$, where each pair $G_i$, $G_j$ with $i \neq j$ shares the same graph $G$, the problem Simultaneous Embedding With Fixed Edges (SEFE) asks whether there exists a planar drawing for each input graph…
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…
This work investigates the parameterized complexity of three related graph modification problems. Given a directed graph, a distinguished vertex, and a positive integer k, Minimum Indegree Deletion asks for a vertex subset of size at most k…
For a positive integer $k$ and graph $G=(V,E)$, a $k$-colouring of $G$ is a mapping $c: V\rightarrow\{1,2,\ldots,k\}$ such that $c(u)\neq c(v)$ whenever $uv\in E$. The $k$-Colouring problem is to decide, for a given $G$, whether a…
We study the parameterized complexity of interdiction problems in graphs. For an optimization problem on graphs, one can formulate an interdiction problem as a game consisting of two players, namely, an interdictor and an evader, who…