## Abstract

The r-size-Ramsey number (Formula presented.) of a graph H is the smallest number of edges a graph G can have such that for every edge-coloring of G with r colors there exists a monochromatic copy of H in G. For a graph H, we denote by H^{q} the graph obtained from H by subdividing its edges with q − 1 vertices each. In a recent paper of Kohayakawa, Retter and Rödl, it is shown that for all constant integers q, r ≥ 2 and every graph H on n vertices and of bounded maximum degree, the r-size-Ramsey number of H^{q} is at most (Formula presented.), for n large enough. We improve upon this result using a significantly shorter argument by showing that (Formula presented.) for any such graph H.

Original language | English |
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Pages (from-to) | 68-78 |

Number of pages | 11 |

Journal | Random Structures and Algorithms |

Volume | 59 |

Issue number | 1 |

DOIs | |

State | Published - Aug 2021 |

## Keywords

- Ramsey theory
- random graphs
- subdivisions