### Abstract

Answering a question of Alon et al., we show that there exists an absolute constant C such that every graph G with maximum degree 5 has a vertex partition into 2 parts, such that the subgraph induced by each part has no component of size greater than C. We obtain similar results for partitioning graphs of given maximum degree into k parts (k > 2) as well. A related theorem is also proved about transversals inducing only small components in graphs of a given maximum degree.

Original language | English |
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Pages (from-to) | 281-297 |

Number of pages | 17 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 88 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jul 2003 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Journal of Combinatorial Theory. Series B*,

*88*(2), 281-297. https://doi.org/10.1016/S0095-8956(03)00031-5

**Bounded size components - Partitions and transversals.** / Haxell, Penny; Szabó, Tibor; Tardos, G.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory. Series B*, vol. 88, no. 2, pp. 281-297. https://doi.org/10.1016/S0095-8956(03)00031-5

}

TY - JOUR

T1 - Bounded size components - Partitions and transversals

AU - Haxell, Penny

AU - Szabó, Tibor

AU - Tardos, G.

PY - 2003/7

Y1 - 2003/7

N2 - Answering a question of Alon et al., we show that there exists an absolute constant C such that every graph G with maximum degree 5 has a vertex partition into 2 parts, such that the subgraph induced by each part has no component of size greater than C. We obtain similar results for partitioning graphs of given maximum degree into k parts (k > 2) as well. A related theorem is also proved about transversals inducing only small components in graphs of a given maximum degree.

AB - Answering a question of Alon et al., we show that there exists an absolute constant C such that every graph G with maximum degree 5 has a vertex partition into 2 parts, such that the subgraph induced by each part has no component of size greater than C. We obtain similar results for partitioning graphs of given maximum degree into k parts (k > 2) as well. A related theorem is also proved about transversals inducing only small components in graphs of a given maximum degree.

UR - http://www.scopus.com/inward/record.url?scp=0038687994&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038687994&partnerID=8YFLogxK

U2 - 10.1016/S0095-8956(03)00031-5

DO - 10.1016/S0095-8956(03)00031-5

M3 - Article

AN - SCOPUS:0038687994

VL - 88

SP - 281

EP - 297

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

IS - 2

ER -