Related papers: On the Complexity of Distance-$d$ Independent Set …
For a fixed integer $r \geq 1$, a distance-$r$ dominating set (D$r$DS) of a graph $G = (V, E)$ is a vertex subset $D \subseteq V$ such that every vertex in $V$ is within distance $r$ from some member of $D$. Given two D$r$DSs $D_s, D_t$ of…
An independent set of a graph $G$ is a vertex subset $I$ such that there is no edge joining any two vertices in $I$. Imagine that a token is placed on each vertex of an independent set of $G$. The $\mathsf{TS}$- ($\mathsf{TS}_k$-)…
The independent set reconfiguration problem (ISReconf) is the problem of determining, for given independent sets I_s and I_t of a graph G, whether I_s can be transformed into I_t by repeatedly applying a prescribed reconfiguration rule that…
In a graph, a vertex dominates itself and its neighbors, and a dominating set is a set of vertices that together dominate the entire graph. Given a graph and two dominating sets of equal size $k$, the {\em Dominating Set Reconfiguration…
Given a graph $G$ and two independent sets $I_s$ and $I_t$ of size $k$, the independent set reconfiguration problem asks whether there exists a sequence of $k$-sized independent sets $I_s = I_0, I_1, I_2, \ldots, I_\ell = I_t$ such that…
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 study the problem of checking the existence of a step-by-step transformation of $d$-regular induced subgraphs in a graph, where $d \ge 0$ and each step in the transformation must follow a fixed reconfiguration rule. Our problem for $d=0$…
Given a graph $G$ and two independent sets of same size, the Independent Set Reconfiguration Problem under token sliding ask whether one can, in a step by step manner, transform the first independent set into the second one. In each step we…
In this article, we revisit the complexity of the reconfiguration of independent sets under the token sliding rule on chordal graphs. In the \textsc{Token Sliding-Connectivity} problem, the input is a graph $G$ and an integer $k$, and the…
Assume we are given a graph $G$, two independent sets $S$ and $T$ in $G$ of size $k \geq 1$, and a positive integer $\ell \geq 1$. The goal is to decide whether there exists a sequence $\langle I_0, I_1, ..., I_\ell \rangle$ of independent…
A vertex-subset graph problem Q defines which subsets of the vertices of an input graph are feasible solutions. A reconfiguration variant of a vertex-subset problem asks, given two feasible solutions S and T of size k, whether it is…
\textsc{Directed Token Sliding} asks, given a directed graph and two sets of pairwise nonadjacent vertices, whether one can reach from one set to the other by repeatedly applying a local operation that exchanges a vertex in the current set…
Reconfiguration problems ask whether one feasible solution can be transformed into another by a sequence of local moves while maintaining feasibility throughout. For integers $d \geq 1$ and $k \geq d+1$, the Distance Coloring problem asks…
Suppose that two independent sets $I$ and $J$ of a graph with $\vert I \vert = \vert J \vert$ are given, and a token is placed on each vertex in $I$. The Sliding Token problem is to determine whether there exists a sequence of independent…
We propose a novel generalization of Independent Set Reconfiguration (ISR): Connected Components Reconfiguration (CCR). In CCR, we are given a graph $G$, two vertex subsets $A$ and $B$, and a multiset $\mathcal{M}$ of positive integers. The…
Suppose that we are given two independent sets I_b and I_r of a graph such that |I_b|=|I_r|, and imagine that a token is placed on each vertex in |I_b|. Then, the sliding token problem is to determine whether there exists a sequence of…
In the Token Sliding problem we are given a graph $G$ and two independent sets $I_s$ and $I_t$ in $G$ of size $k \geq 1$. The goal is to decide whether there exists a sequence $\langle I_1, I_2, \ldots, I_\ell \rangle$ of independent sets…
We study reconfiguration of independent sets in interval graphs under the token sliding rule. We show that if two independent sets of size $k$ are reconfigurable in an $n$-vertex interval graph, then there is a reconfiguration sequence of…
For a positive integer $r$, a distance-$r$ independent set in an undirected graph $G$ is a set $I\subseteq V(G)$ of vertices pairwise at distance greater than $r$, while a distance-$r$ dominating set is a set $D\subseteq V(G)$ such that…
We study the following independent set reconfiguration problem, called TAR-Reachability: given two independent sets $I$ and $J$ of a graph $G$, both of size at least $k$, is it possible to transform $I$ into $J$ by adding and removing…