# On Girth and the Parameterized Complexity of Token Sliding and Token Jumping

@article{Bartier2020OnGA, title={On Girth and the Parameterized Complexity of Token Sliding and Token Jumping}, author={Valentin Bartier and Nicolas Bousquet and Cl{\'e}ment Dallard and Kyle Lomer and Amer E. Mouawad}, journal={Algorithmica}, year={2020}, volume={83}, pages={2914 - 2951} }

In the Token Jumping problem we are given a graph G=(V,E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G = (V,E)$$\end{document} and two independent sets S and T of G, each of size k≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage…

## 6 Citations

### Token sliding on graphs of girth five

- MathematicsWG
- 2022

. 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 ≥ 1. The goal is to decide whether there exists a sequence (cid:104) I 1 , I 2 , . . . , I…

### A survey on the parameterized complexity of the independent set and (connected) dominating set reconfiguration problems

- Mathematics, Computer ScienceArXiv
- 2022

This work considers reconﬁguration variants of three fundamental underlying graph vertex-subset problems, namely Independent Set, Dominating Set, and Connected Dominating set, and surveys both older and more recent work on the parameterized complexity of all three problems when parameterized by the number of tokens k.

### Galactic Token Sliding

- Mathematics, Computer ScienceESA
- 2022

This work introduces a new model for the reconfiguration of independent sets, which it is believed is of independent interest and could potentially help in resolving the remaining open questions concerning the (parameterized) complexity of Token Sliding.

### Independent set reconfiguration on directed graphs

- Mathematics, Computer ScienceMFCS
- 2022

A linear-time algorithm for the problem on directed graphs whose underlying undirected graphs are trees, which are called polytrees, and a characterization of yes-instances based on the existence of a certain set of directed paths, which admits an e-cient algorithm.

### Refuting FPT Algorithms for Some Parameterized Problems Under Gap-ETH

- MathematicsIPEC
- 2021

In this article we study a well-known problem, called Bipartite Token Jumping and not-so-well known problem(s), which we call, Half (Induced-) Subgraph , and show that under Gap-ETH, these problems…

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