Related papers: Reconfiguration on sparse graphs
Numerous problems consisting in identifying vertices in graphs using distances are useful in domains such as network verification and graph isomorphism. Unifying them into a meta-problem may be of main interest. We introduce here a…
We prove that Graph Isomorphism and Canonization in graphs excluding a fixed graph $H$ as a minor can be solved by an algorithm working in time $f(H)\cdot n^{O(1)}$, where $f$ is some function. In other words, we show that these problems…
We algorithmize the recent structural characterization for claw-free graphs by Chudnovsky and Seymour. Building on this result, we show that Dominating Set on claw-free graphs is (i) fixed-parameter tractable and (ii) even possesses a…
The Kneser graph $K(n,k)$ is defined for integers $n$ and $k$ with $n \geq 2k$ as the graph whose vertices are all the $k$-subsets of $\{1,2,\ldots,n\}$ where two such sets are adjacent if they are disjoint. A classical result of Lov\'asz…
In the deletion version of the list homomorphism problem, we are given graphs G and H, a list L(v) that is a subset of V(H) for each vertex v of G, and an integer k. The task is to decide whether there exists a subset W of V(G) of size at…
{\sc Directed Feedback Vertex Set (DFVS)} is a fundamental computational problem that has received extensive attention in parameterized complexity. In this paper, we initiate the study of a wide generalization, the {\sc ${\cal H}$-free SCC…
Given a graph $G = (V, E)$, a non-empty set $S \subseteq V$ is a defensive alliance, if for every vertex $v \in S$, the majority of its closed neighbours are in $S$, that is, $|N_G[v] \cap S| \geq |N_G[v] \setminus S|$. The decision version…
We introduce in a general setting a dynamic programming method for solving reconfiguration problems. Our method is based on contracted solution graphs, which are obtained from solution graphs by performing an appropriate series of edge…
The computational complexity of the graph isomorphism problem is considered to be a major open problem in theoretical computer science. It is known that testing isomorphism of chordal graphs is polynomial-time equivalent to the general…
For fixed integers $r,\ell \geq 0$, a graph $G$ is called an {\em $(r,\ell)$-graph} if the vertex set $V(G)$ can be partitioned into $r$ independent sets and $\ell$ cliques. This brings us to the following natural parameterized questions:…
Parameterized algorithms are a very useful tool for dealing with NP-hard problems on graphs. Yet, to properly utilize parameterized algorithms it is necessary to choose the right parameter based on the type of problem and properties of the…
The Directed Feedback Vertex Set problem (DFVS) asks whether it is possible to remove at most $k$ vertices from a directed graph to make it acyclic. Whether DFVS is fixed-parameter tractable was a long-standing open problem in parameterized…
A vertex set $S$ of a graph $G$ is geodetic if every vertex of $G$ lies on a shortest path between two vertices in $S$. Given a graph $G$ and $k \in \mathbb N$, the NP-hard Geodetic Set problem asks whether there is a geodetic set of size…
We study the parameterized complexity of the T(h+1)-Free Edge Deletion problem. Given a graph G and integers k and h, the task is to delete at most k edges so that every connected component of the resulting graph has size at most h. The…
A graph $G=(V,E)$ is called equidominating if there exists a value $t \in \mathbb{N}$ and a weight function $\omega : V \rightarrow \mathbb{N}$ such that the total weight of a subset $D\subseteq V$ is equal to $t$ if and only if $D$ is a…
In the Dominated Cluster Deletion problem, we are given an undirected graph $G$ and integers $k$ and $d$ and the question is to decide whether there exists a set of at most $k$ vertices whose removal results in a graph in which each…
The dominating set reconfiguration problem is defined as determining, for a given dominating set problem and two among its feasible solutions, whether one is reachable from the other via a sequence of feasible solutions subject to a certain…
Inversion of a directed graph $D$ with respect to a vertex subset $Y$ is the directed graph obtained from $D$ by reversing the direction of every arc whose endpoints both lie in $Y$. More generally, the inversion of $D$ with respect to a…
Many combinatorial problems can be solved in time $O^*(c^{tw})$ on graphs of treewidth $tw$, for a problem-specific constant $c$. In several cases, matching upper and lower bounds on $c$ are known based on the Strong Exponential Time…
Numerous applications in scheduling, such as resource allocation or steel manufacturing, can be modeled using the NP-hard Independent Set problem (given an undirected graph and an integer k, find a set of at least k pairwise non-adjacent…