## Abstract

For [Formula presented] given graphs [Formula presented], [Formula presented], the [Formula presented]-color Ramsey number, denoted by [Formula presented], is the smallest integer [Formula presented] such that if we arbitrarily color the edges of a complete graph of order [Formula presented] with [Formula presented] colors, then it always contains a monochromatic copy of [Formula presented] colored with [Formula presented], for some [Formula presented]. Let [Formula presented] be a cycle of length [Formula presented] and [Formula presented] a star of order [Formula presented]. In this paper, firstly we give a general upper bound of [Formula presented]. In particular, for the 3-color case, we have [Formula presented] and this bound is tight in some sense. Furthermore, we prove that [Formula presented] for all [Formula presented] and [Formula presented], and if [Formula presented] is a prime power, then the equality holds.

Original language | English |
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Pages (from-to) | 285-291 |

Number of pages | 7 |

Journal | Discrete Mathematics |

Volume | 342 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2019 |

## Keywords

- Multicolor Ramsey number
- Polarity graph
- Quadrilateral
- Singer difference set
- Star

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics