Related papers: Complexity of Token Swapping and its Variants
The task of the broadcast problem is, given a graph G and a source vertex s, to compute the minimum number of rounds required to disseminate a piece of information from s to all vertices in the graph. It is assumed that, at each round, an…
For graphs $G$ and $H$, a \emph{homomorphism} from $G$ to $H$ is an edge-preserving mapping from the vertex set of $G$ to the vertex set of $H$. For a fixed graph $H$, by \textsc{Hom($H$)} we denote the computational problem which asks…
A stable or locally-optimal cut of a graph is a cut whose weight cannot be increased by changing the side of a single vertex. In this paper we study Minimum Stable Cut, the problem of finding a stable cut of minimum weight. Since this…
The $k$-colouring reconfiguration problem asks whether, for a given graph $G$, two proper $k$-colourings $\alpha$ and $\beta$ of $G$, and a positive integer $\ell$, there exists a sequence of at most $\ell+1$ proper $k$-colourings of $G$…
In this paper we study the parameterized complexity of two well-known permutation group problems which are NP-complete. 1. Given a permutation group G=<S>, subgroup of $S_n$, and a parameter $k$, find a permutation $\pi$ in G such that…
We analyze two classic variants of the Traveling Salesman Problem using the toolkit of fine-grained complexity. Our first set of results is motivated by the Bitonic TSP problem: given a set of $n$ points in the plane, compute a shortest…
In this paper we consider a variation of a recoloring problem, called the Color-Fixing. Let us have some non-proper $r$-coloring $\varphi$ of a graph $G$. We investigate the problem of finding a proper $r$-coloring of $G$, which is "the…
For a connected graph $G = (V, E)$ and $s, t \in V$, a non-separating $s$-$t$ path is a path $P$ between $s$ and $t$ such that the set of vertices of $P$ does not separate $G$, that is, $G - V(P)$ is connected. An $s$-$t$ path is…
The NP-hard Odd Cycle Transversal problem asks for a minimum vertex set whose removal from an undirected input graph $G$ breaks all odd cycles, and thereby yields a bipartite graph. The problem is well-known to be fixed-parameter tractable…
We study the parameterized complexity of #IndSub($\Phi$), where given a graph $G$ and an integer $k$, the task is to count the number of induced subgraphs on $k$ vertices that satisfy the graph property $\Phi$. Focke and Roth [STOC 2022]…
The $k$-Even Set problem is a parameterized variant of the Minimum Distance Problem of linear codes over $\mathbb F_2$, which can be stated as follows: given a generator matrix $\mathbf A$ and an integer $k$, determine whether the code…
We study the coloring problem: Given a graph G, decide whether $c(G) \leq q$ or $c(G) \ge Q$, where c(G) is the chromatic number of G. We derive conditional hardness for this problem for any constant $3 \le q < Q$. For $q\ge 4$, our result…
The problem of matching a query string to a directed graph, whose vertices are labeled by strings, has application in different fields, from data mining to computational biology. Several variants of the problem have been considered,…
We show that Closest Substring, one of the most important problems in the field of biological sequence analysis, is W[1]-hard when parameterized by the number k of input strings (and remains so, even over a binary alphabet). This problem is…
We address the problem of testing whether a given dynamic graph is temporally connected, {\it i.e} a temporal path (also called a {\em journey}) exists between all pairs of vertices. We consider a discrete version of the problem, where the…
As the class $\mathcal T_4$ of graphs of twin-width at most 4 contains every finite subgraph of the infinite grid and every graph obtained by subdividing each edge of an $n$-vertex graph at least $2 \log n$ times, most NP-hard graph…
A square coloring of a graph $G$ is a coloring of the square $G^2$ of $G$, that is, a coloring of the vertices of $G$ such that any two vertices that are at distance at most $2$ in $G$ receive different colors. We investigate the complexity…
We study the knapsack problem with graph theoretic constraints. That is, we assume that there exists a graph structure on the set of items of knapsack and the solution also needs to satisfy certain graph theoretic properties on top of…
Various applications of graphs, in particular applications related to finding shortest paths, naturally get inputs with real weights on the edges. However, for algorithmic or visualization reasons, inputs with integer weights would often be…
The independent set reconfiguration problem asks whether one can transform one given independent set of a graph into another, by changing vertices one by one in such a way the intermediate sets remain independent. Extremal problems on…