Related papers: Token Sliding on Chordal Graphs
We study two fundamental problems related to finding subgraphs: (1) given graphs G and H, Subgraph Test asks if H is isomorphic to a subgraph of G, (2) given graphs G, H, and an integer t, Packing asks if G contains t vertex-disjoint…
The square of a graph $G$, denoted $G^2$, is obtained from $G$ by putting an edge between two distinct vertices whenever their distance is two. Then $G$ is called a square root of $G^2$. Deciding whether a given graph has a square root is…
In the solution discovery variant of a vertex (edge) subset problem $\Pi$ on graphs, we are given an initial configuration of tokens on the vertices (edges) of an input graph $G$ together with a budget $b$. The question is whether we can…
We consider the problem of testing graph cluster structure: given access to a graph $G=(V, E)$, can we quickly determine whether the graph can be partitioned into a few clusters with good inner conductance, or is far from any such graph?…
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…
We prove a characterization of all polynomial-time computable queries on the class of interval graphs by sentences of fixed-point logic with counting. More precisely, it is shown that on the class of unordered interval graphs, any query is…
A monitoring edge-geodetic set of a graph is a subset $M$ of its vertices such that for every edge $e$ in the graph, deleting $e$ increases the distance between at least one pair of vertices in $M$. We study the following computational…
We investigate the computational complexity of finding temporally disjoint paths or walks in temporal graphs. There, the edge set changes over discrete time steps and a temporal path (resp. walk) uses edges that appear at monotonically…
In the Token Swapping problem we are given a graph with a token placed on each vertex. Each token has exactly one destination vertex, and we try to move all the tokens to their destinations, using the minimum number of swaps, i.e.,…
In reconfiguration problems, we are given two feasible solutions to a graph problem and asked whether one can be transformed into the other via a sequence of feasible intermediate solutions under a given reconfiguration rule. While earlier…
We show that edge-clique graphs of cocktail party graphs have unbounded rankwidth. This, and other observations lead us to conjecture that the edge-clique cover problem is NP-complete for cographs. We show that the independent set problem…
Imagine that unlabelled tokens are placed on the edges of a graph, such that no two tokens are placed on incident edges. A token can jump to another edge if the edges having tokens remain independent. We study the problem of determining the…
Seidel's switching is a graph operation which makes a given vertex adjacent to precisely those vertices to which it was non-adjacent before, while keeping the rest of the graph unchanged. Two graphs are called switching-equivalent if one…
In the GEODETIC SET problem, an input is a (di)graph $G$ and integer $k$, and the objective is to decide whether there exists a vertex subset $S$ of size $k$ such that any vertex in $V(G)\setminus S$ lies on a shortest (directed) path…
It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties…
We consider the ideal orientation problem in planar graphs. In this problem, we are given an undirected graph $G$ with positive edge lengths and $k$ pairs of distinct vertices $(s_1, t_1), \dots, (s_k, t_k)$ called terminals, and we want to…
The Induced Graph Matching problem asks to find k disjoint induced subgraphs isomorphic to a given graph H in a given graph G such that there are no edges between vertices of different subgraphs. This problem generalizes the classical…
Simultaneous Geometric Embedding (SGE) asks whether, for a given collection of graphs on the same vertex set V, there is an embedding of V in the plane that admits a crossing-free drawing with straightline edges for each of the given…
In a reconfiguration problem, we are given two feasible solutions of a combinatorial problem and our goal is to determine whether it is possible to reconfigure one into the other, with the steps dictated by specific reconfiguration rules.…
We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on…