### Abstract

The Ramsey number of a graph G is the least number t for which it is true that whenever the edges of the complete graph on t vertices are colored in an arbitrary fashion using two colors, say red and blue, then it is always the case that either the red subgraph contains G or the blue subgraph contains G. A conjecture of P. Erdös and S. Burr is settled in the affirmative by proving that for each d ≥ 1, there exists a constant c so that if G is any graph on n vertices with maximum degree d, then the Ramsey number of G is at most cn.

Original language | English |
---|---|

Pages (from-to) | 239-243 |

Number of pages | 5 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 34 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1983 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Journal of Combinatorial Theory. Series B*,

*34*(3), 239-243. https://doi.org/10.1016/0095-8956(83)90037-0

**The Ramsey number of a graph with bounded maximum degree.** / Chvatál, C.; Rödl, V.; Szemerédi, E.; Trotter, W. T.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory. Series B*, vol. 34, no. 3, pp. 239-243. https://doi.org/10.1016/0095-8956(83)90037-0

}

TY - JOUR

T1 - The Ramsey number of a graph with bounded maximum degree

AU - Chvatál, C.

AU - Rödl, V.

AU - Szemerédi, E.

AU - Trotter, W. T.

PY - 1983

Y1 - 1983

N2 - The Ramsey number of a graph G is the least number t for which it is true that whenever the edges of the complete graph on t vertices are colored in an arbitrary fashion using two colors, say red and blue, then it is always the case that either the red subgraph contains G or the blue subgraph contains G. A conjecture of P. Erdös and S. Burr is settled in the affirmative by proving that for each d ≥ 1, there exists a constant c so that if G is any graph on n vertices with maximum degree d, then the Ramsey number of G is at most cn.

AB - The Ramsey number of a graph G is the least number t for which it is true that whenever the edges of the complete graph on t vertices are colored in an arbitrary fashion using two colors, say red and blue, then it is always the case that either the red subgraph contains G or the blue subgraph contains G. A conjecture of P. Erdös and S. Burr is settled in the affirmative by proving that for each d ≥ 1, there exists a constant c so that if G is any graph on n vertices with maximum degree d, then the Ramsey number of G is at most cn.

UR - http://www.scopus.com/inward/record.url?scp=0003044449&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0003044449&partnerID=8YFLogxK

U2 - 10.1016/0095-8956(83)90037-0

DO - 10.1016/0095-8956(83)90037-0

M3 - Article

VL - 34

SP - 239

EP - 243

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

IS - 3

ER -