## Abstract

For k given graphs H_{1},…,H_{k}, k≥2, the k-color Ramsey number, denoted by R(H_{1},…,H_{k}), is the smallest integer N such that if we arbitrarily color the edges of a complete graph of order N with k colors, then it always contains a monochromatic copy of H_{i} colored with i, for some 1≤i≤k. Let C_{m} be a cycle of length m, K_{1,n} a star of order n+1 and W_{n} a wheel of order n+1. In this paper, by using algebraic and probabilistic methods, we first give two lower bounds for (k+1)-color Ramsey number R(C_{4},…,C_{4},K_{1,n}) for some special n, which shows the upper bound due to Zhang et al. (2019) is tight in some sense, and then establish a general lower bound for R(C_{4},…,C_{4},K_{1,n}) in terms of n and k, which extends the classical result of Burr et al. (1989). Moreover, we show that R(C_{4},…,C_{4},K_{1,n})=R(C_{4},…,C_{4},W_{n}) for sufficiently large n.

Original language | English |
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Article number | 101999 |

Journal | Finite Fields and Their Applications |

Volume | 79 |

DOIs | |

Publication status | Published - Mar 2022 |

## Keywords

- Galois field
- Multicolor Ramsey number
- Quadrilateral
- Random graph
- Singer difference set
- Star
- Wheel

## ASJC Scopus subject areas

- Theoretical Computer Science
- Algebra and Number Theory
- Engineering(all)
- Applied Mathematics