## Abstract

Given two colorings of a graph, we consider the following problem: can we recolor the graph from one coloring to the other through a series of elementary changes, such that the graph is properly colored after each step? We introduce the notion of distributed recoloring: The input graph represents a network of computers that needs to be recolored. Initially, each node is aware of its own input color and target color. The nodes can exchange messages with each other, and eventually each node has to stop and output its own recoloring schedule, indicating when and how the node changes its color. The recoloring schedules have to be globally consistent so that the graph remains properly colored at each point, and we require that adjacent nodes do not change their colors simultaneously. We are interested in the following questions: How many communication rounds are needed (in the deterministic LOCAL model of distributed computing) to find a recoloring schedule? What is the length of the recoloring schedule? And how does the picture change if we can use extra colors to make recoloring easier? The main contributions of this work are related to distributed recoloring with one extra color in the following graph classes: trees, 3-regular graphs, and toroidal grids.

Original language | English |
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Title of host publication | 32nd International Symposium on Distributed Computing, DISC 2018 |

Editors | Ulrich Schmid, Josef Widder |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

Pages | 1-17 |

ISBN (Electronic) | 9783959770927 |

DOIs | |

Publication status | Published - 1 Oct 2018 |

MoE publication type | A4 Article in a conference publication |

Event | International Symposium on Distributed Computing - New Orleans, United States Duration: 15 Oct 2018 → 19 Oct 2018 Conference number: 32 http://www.disc-conference.org/wp/disc2018/ |

### Publication series

Name | Leibniz International Proceedings in Informatics (LIPIcs) |
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Publisher | Schloss Dagstuhl--Leibniz-Zentrum für Informatik |

Volume | 121 |

ISSN (Electronic) | 1868-8969 |

### Conference

Conference | International Symposium on Distributed Computing |
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Abbreviated title | DISC |

Country/Territory | United States |

City | New Orleans |

Period | 15/10/2018 → 19/10/2018 |

Internet address |

## Keywords

- And phrases Distributed Systems
- Graph Algorithms
- Local Computations