## Abstract

In graph coloring problems, the goal is to assign a positive integer color to each vertex of an input graph such that adjacent vertices do not receive the same color assignment. For classic graph coloring, the goal is to minimize the maximum color used, and for the sum coloring problem, the goal is to minimize the sum of colors assigned to all input vertices. In the offline variant, the entire graph is presented at once, and in online problems, one vertex is presented for coloring at each time, and the only information is the identity of its neighbors among previously known vertices. In batched graph coloring, vertices are presented in k batches, for a fixed integer k ≥ 2, such that the vertices of a batch are presented as a set, and must be colored before the vertices of the next batch are presented. This last model is an intermediate model, which bridges between the two extreme scenarios of the online and offline models. We provide several results, including a general result for sum coloring and results for the classic graph coloring problem on restricted graph classes: We show tight bounds for any graph class containing trees as a subclass (e.g., forests, bipartite graphs, planar graphs, and perfect graphs), and a surprising result for interval graphs and k = 2, where the value of the (strict and asymptotic) competitive ratio depends on whether the graph is presented with its interval representation or not.

Original language | English |
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Title of host publication | Approximation and Online Algorithms - 14th International Workshop, WAOA 2016, Revised Selected Papers |

Editors | Monaldo Mastrolilli, Klaus Jansen |

Publisher | Springer Verlag |

Pages | 52-64 |

Number of pages | 13 |

ISBN (Print) | 9783319517407 |

DOIs | |

State | Published - 2017 |

Event | 14th International Workshop on Approximation and Online Algorithms, WAOA 2016 - Aarhus, Denmark Duration: 25 Aug 2016 → 26 Aug 2016 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10138 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 14th International Workshop on Approximation and Online Algorithms, WAOA 2016 |
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Country/Territory | Denmark |

City | Aarhus |

Period | 25/08/16 → 26/08/16 |

### Bibliographical note

Funding Information:J. Boyar, L.M. Favrholdt and K.S. Larsen—Supported in part by the Danish Council for Independent Research, Natural Sciences, grant DFF-1323-00247, and the Villum Foundation, grant VKR023219.

Publisher Copyright:

© Springer International Publishing AG 2017.

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science (all)