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Related papers: Token sliding independent set reconfiguration on b…

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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

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…

Combinatorics · Mathematics 2021-05-10 Marcin Briański , Stefan Felsner , Jędrzej Hodor , Piotr Micek

We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transformation, we consider…

Data Structures and Algorithms · Computer Science 2014-12-15 Takehiro Ito , Hirotaka Ono , Yota Otachi

We settle the complexity of the Independent Set Reconfiguration problem on bipartite graphs under all three commonly studied reconfiguration models. We show that under the token jumping or token addition/removal model the problem is…

Computational Complexity · Computer Science 2017-07-11 Daniel Lokshtanov , Amer E. Mouawad

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…

Discrete Mathematics · Computer Science 2025-05-01 Jona Dirks , Alexandre Vigny

We continue the study of graph classes in which the treewidth can only be large due to the presence of a large clique, and, more specifically, of graph classes with bounded tree-independence number. In [Dallard, Milani\v{c}, and…

Data Structures and Algorithms · Computer Science 2022-09-27 Martin Milanič , Paweł Rzążewski

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

In this note, we consider the problem of finding a step-by-step transformation between two longest increasing subsequences in a sequence, namely Longest Increasing Subsequence Reconfiguration. We give a polynomial-time algorithm for…

Data Structures and Algorithms · Computer Science 2023-10-03 Yuuki Aoike , Masashi Kiyomi , Yasuaki Kobayashi , Yota Otachi

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

We present the first results on the complexity of the reconfiguration of vertex separators under the three most popular rules: token addition/removal, token jumping, and token sliding. We show that, aside from some trivially negative…

Computational Complexity · Computer Science 2020-04-24 Guilherme C. M. Gomes , Sérgio H. Nogueira , Vinicius F. dos Santos

In the Independent set problem, the input is a graph $G$, every vertex has a non-negative integer weight, and the task is to find a set $S$ of pairwise non-adjacent vertices, maximizing the total weight of the vertices in $S$. We give an…

Data Structures and Algorithms · Computer Science 2015-09-02 Daniel Lokshtanov , Marcin Pilipczuk , Erik Jan van Leeuwen

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

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…

Computational Complexity · Computer Science 2017-06-30 Nicolas Bousquet , Arnaud Mary , Aline Parreau

In the classic Maximum Weight Independent Set problem we are given a graph $G$ with a nonnegative weight function on vertices, and the goal is to find an independent set in $G$ of maximum possible weight. While the problem is NP-hard in…

Data Structures and Algorithms · Computer Science 2020-03-24 Andrzej Grzesik , Tereza Klimošová , Marcin Pilipczuk , Michał Pilipczuk

In this paper, we present novel algorithms that efficiently compute a shortest reconfiguration sequence between two given dominating sets in trees and interval graphs under the Token Sliding model. In this problem, a graph is provided along…

Data Structures and Algorithms · Computer Science 2023-07-21 Jan Matyáš Křišťan , Jakub Svoboda

In combinatorial reconfiguration, the reconfiguration problems on a vertex subset (e.g., an independent set) are well investigated. In these problems, some tokens are placed on a subset of vertices of the graph, and there are three natural…

Computational Complexity · Computer Science 2021-09-07 Masaaki Kanzaki , Yota Otachi , Ryuhei Uehara

Given a graph where every vertex has exactly one labeled token, how can we most quickly execute a given permutation on the tokens? In (sequential) token swapping, the goal is to use the shortest possible sequence of swaps, each of which…

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…

Combinatorics · Mathematics 2024-11-22 Jan Matyáš Křišťan , Jakub Svoboda

Given a graph $G$, and terminal vertices $s$ and $t$, the TRACKING PATHS problem asks to compute a minimum number of vertices to be marked as trackers, such that the sequence of trackers encountered in each s-t path is unique. TRACKING…

Data Structures and Algorithms · Computer Science 2020-02-19 Pratibha Choudhary

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