### Abstract

In this study we consider a Ramsey property of random d-regular graphs, g(n, d). Let r ≥ 2 be fixed. Then w.h.p. the edges of g(n, 2r) can be colored such that every monochromatic component has order o (n). On the other hand, there exists a constant γ > 0 such that w.h.p., every r-coloring of the edges of g(n, 2r + 1) must contain a monochromatic cycle of length at least γn. We prove an analogous result for random k -out graphs.

Original language | English |
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Pages (from-to) | 363-371 |

Number of pages | 9 |

Journal | Journal of Graph Theory |

Volume | 93 |

Issue number | 3 |

DOIs | |

State | Published - 1 Mar 2020 |

### Keywords

- monochromatic components
- random k-out graphs
- random regular graphs

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## Cite this

Anastos, M., & Bal, D. (2020). A Ramsey property of random regular and k-out graphs.

*Journal of Graph Theory*,*93*(3), 363-371. https://doi.org/10.1002/jgt.22491