Related papers: A simple quadratic kernel for Token Jumping on sur…

Let $G$ be a planar graph and $I_s$ and $I_t$ be two independent sets in $G$, each of size $k$. We begin with a "token" on each vertex of $I_s$ and seek to move all tokens to $I_t$, by repeated "token jumping", removing a single token from…

Given two $k$-independent sets $I$ and $J$ of a graph $G$, one can ask if it is possible to transform the one into the other in such a way that, at any step, we replace one vertex of the current independent set by another while keeping the…

Given two independent sets $I, J$ of a graph $G$, and imagine that a token (coin) is placed at each vertex of $I$. The Sliding Token problem asks if one could transform $I$ to $J$ via a sequence of elementary steps, where each step requires…

Let I be an independent set of a graph G. Imagine that a token is located on any vertex of I. We can now move the tokens of I along the edges of the graph as long as the set of tokens still defines an independent set of G. Given two…

In the Token Jumping problem we are given a graph $G = (V,E)$ and two independent sets $S$ and $T$ of $G$, each of size $k \geq 1$. The goal is to determine whether there exists a sequence of $k$-sized independent sets in $G$, $\langle S_0,…

Suppose that we are given two independent sets $I_0$ and $I_r$ of a graph such that $|I_0| = |I_r|$, and imagine that a token is placed on each vertex in $I_0$. The token jumping problem is to determine whether there exists a sequence of…

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 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…

Let $S$ be an independent set of a simple undirected graph $G$. Suppose that each vertex of $S$ has a token placed on it. The tokens are allowed to be moved, one at a time, by sliding along the edges of $G$, so that after each move, the…

Given a graph $G$ and two independent sets of $G$, the independent set reconfiguration problem asks whether one independent set can be transformed into the other by moving a single vertex at a time, such that at each intermediate step we…

Fix a positive integer $r$, and a graph $G$ that is $K_{3,r}$-minor-free. Let $I_s$ and $I_t$ be two independent sets in $G$, each of size $k$. We begin with a ``token'' on each vertex of $I_s$ and seek to move all tokens to $I_t$, by…

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…

Reconfiguration problems involve determining whether two given configurations can be transformed into each other under specific rules. The Token Sliding problem asks whether, given two different set of tokens on vertices of a graph $G$, we…

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 $\mathsf{TS}$- ($\mathsf{TS}_k$-)…

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…

In reconfiguration, we are given two solutions to a graph problem, such as Vertex Cover or Dominating Set, with each solu tion represented by a placement of tokens on vertices of the graph. Our task is to reconfigure one into the other…

The graph isomorphism (GI) problem is the computational problem of finding a permutation of vertices of a given graph $G_1$ that transforms $G_1$ to another given graph $G_2$ and preserves the adjacency. In this work, we propose a quantum…

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…

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…

We study the problem of reconfiguring one minimum $s$-$t$-separator $A$ into another minimum $s$-$t$-separator $B$ in some $n$-vertex graph $G$ containing two non-adjacent vertices $s$ and $t$. We consider several variants of the problem as…