### Abstract

We prove that for every graph H, if a graph G has no H minor, then V(G) can be partitioned into three sets such that the subgraph induced on each set has no component of size larger than a function of H and the maximum degree of G. This answers a question of Esperet and Joret and improves a result of Alon, Ding, Oporowski and Vertigan and a result of Esperet and Joret. As a corollary, for every positive integer t, if a graph G has no K_{t+1} minor, then V(G) can be partitioned into 3t sets such that the subgraph induced on each set has no component of size larger than a function of t. This corollary improves a result of Wood.

Original language | English (US) |
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Pages (from-to) | 133-138 |

Number of pages | 6 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 49 |

DOIs | |

State | Published - Nov 2015 |

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Keywords

- Coloring
- Graph minors
- Partitioning

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## Cite this

Liu, C. H., & Oum, S. I. (2015). Partitioning H-minor free graphs into three subgraphs with no large components.

*Electronic Notes in Discrete Mathematics*,*49*, 133-138. https://doi.org/10.1016/j.endm.2015.06.020