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A set of vertices in a graph is c-colorable if the subgraph induced by the set has a proper c-coloring. In this paper, we study the problem of finding a step-by-step transformation (reconfiguration) between two c-colorable sets in the same…

Data Structures and Algorithms · Computer Science 2018-02-20 Takehiro Ito , Yota Otachi

For a fixed positive integer $d \geq 2$, a distance-$d$ independent set (D$d$IS) of a graph is a vertex subset whose distance between any two members is at least $d$. Imagine that there is a token placed on each member of a D$d$IS. Two…

Data Structures and Algorithms · Computer Science 2024-06-19 Duc A. Hoang

Let $\mathcal{Q}$ be a vertex subset problem on graphs. In a reconfiguration variant of $\mathcal{Q}$ we are given a graph $G$ and two feasible solutions $S_s, S_t\subseteq V(G)$ of $\mathcal{Q}$ with $|S_s|=|S_t|=k$. The problem is to…

Discrete Mathematics · Computer Science 2018-09-12 Sebastian Siebertz

Given a Boolean formula and a satisfying assignment, a flip is an operation that changes the value of a variable in the assignment so that the resulting assignment remains satisfying. We study the problem of computing the shortest sequence…

Computational Complexity · Computer Science 2014-05-28 Amer E. Mouawad , Naomi Nishimura , Vinayak Pathak , Venkatesh Raman

We study the following variant of the 15 puzzle. Given a graph and two token placements on the vertices, we want to find a walk of the minimum length (if any exists) such that the sequence of token swappings along the walk obtains one of…

Data Structures and Algorithms · Computer Science 2025-07-30 Hironori Kiya , Yuto Okada , Hirotaka Ono , Yota Otachi

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…

Discrete Mathematics · Computer Science 2025-07-16 Jona Dirks , Alexandre Vigny

We study the classic sliding cube model for programmable matter under parallel reconfiguration in three dimensions, providing novel algorithmic and surprising complexity results in addition to generalizing the best known bounds from two to…

Computational Geometry · Computer Science 2026-03-10 Hugo A. Akitaya , Joseph Dorfer , Peter Kramer , Christian Rieck , Gabriel Shahrouzi , Frederick Stock

We study the dominating set reconfiguration problem with the token sliding rule. It consists, given a graph G=(V,E) and two dominating sets D_s and D_t of G, in determining if there exists a sequence S=<D_1:=D_s,...,D_l:=D_t> of dominating…

Combinatorics · Mathematics 2021-02-23 Nicolas Bousquet , Alice Joffard

The degree-constrained subgraph problem asks for a subgraph of a given graph such that the degree of each vertex is within some specified bounds. We study the following reconfiguration variant of this problem: Given two solutions to a…

Discrete Mathematics · Computer Science 2015-08-07 Moritz Mühlenthaler

The problem \textsc{Token Jumping} asks whether, given a graph $G$ and two independent sets of \emph{tokens} $I$ and $J$ of $G$, we can transform $I$ into $J$ by changing the position of a single token in each step and having an independent…

Data Structures and Algorithms · Computer Science 2026-02-13 Daniel W. Cranston , Moritz Mühlenthaler , Benjamin Peyrille

A rerouting sequence is a sequence of shortest st-paths such that consecutive paths differ in one vertex. We study the the Shortest Path Rerouting Problem, which asks, given two shortest st-paths P and Q in a graph G, whether a rerouting…

Data Structures and Algorithms · Computer Science 2015-03-20 Paul Bonsma

The problems of Permutation Routing via Matching and Token Swapping are reconfiguration problems on graphs. This paper is concerned with the complexity of those problems and a colored variant. For a given graph where each vertex has a…

Computational Complexity · Computer Science 2017-09-13 Jun Kawahara , Toshiki Saitoh , Ryo Yoshinaka

Given a graph $G$ and two spanning trees $T$ and $T'$ in $G$, Spanning Tree Reconfiguration asks whether there is a step-by-step transformation from $T$ to $T'$ such that all intermediates are also spanning trees of $G$, by exchanging an…

Combinatorics · Mathematics 2024-09-13 Tesshu Hanaka , Yuni Iwamasa , Yasuaki Kobayashi , Yuto Okada , Rin Saito

In the Independent Set Reconfiguration problem under the Token Addition/Removal rule, given a graph $G$ and two independent sets $I$ and $J$ of $G$, we want to transform $I$ into $J$ by adding and removing vertices, such that all the sets…

Data Structures and Algorithms · Computer Science 2026-04-30 Hung P. Hoang , Naoto Ohsaka , Rin Saito , Yuma Tamura

The input to the token swapping problem is a graph with vertices $v_1, v_2, \ldots, v_n$, and $n$ tokens with labels $1, 2, \ldots, n$, one on each vertex. The goal is to get token $i$ to vertex $v_i$ for all $i= 1, \ldots, n$ using a…

Given a static vertex-selection problem (e.g. independent set, dominating set) on a graph, we can define a corresponding temporally satisfying reconfiguration problem on a temporal graph which asks for a sequence of solutions to the…

Data Structures and Algorithms · Computer Science 2025-09-22 Tom Davot , Jessica Enright , Laura Larios-Jones

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…

Computational Complexity · Computer Science 2025-10-29 Shuichi Hirahara , Naoto Ohsaka , Tatsuhiro Suga , Akira Suzuki , Yuma Tamura , Xiao Zhou

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…

Discrete Mathematics · Computer Science 2015-03-12 Takehiro Ito , Marcin Kamiński , Hirotaka Ono

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…

Data Structures and Algorithms · Computer Science 2026-03-10 Niranka Banerjee , Duc A. Hoang

In this paper, we investigate the computational complexity of subgraph reconfiguration problems in directed graphs. More specifically, we focus on the problem of reconfiguring arborescences in a digraph, where an arborescence is a directed…

Data Structures and Algorithms · Computer Science 2023-03-16 Takehiro Ito , Yuni Iwamasa , Yasuaki Kobayashi , Yu Nakahata , Yota Otachi , Kunihiro Wasa