### 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 |
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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 - Jun 1983 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

Chvatál, C., Rödl, V., Szemerédi, E., & Trotter, W. T. (1983). The Ramsey number of a graph with bounded maximum degree.

*Journal of Combinatorial Theory, Series B*,*34*(3), 239-243. https://doi.org/10.1016/0095-8956(83)90037-0