## Almost-rainbow edge-colorings of some small subgraphs

dc.contributor.author | Elliot Krop | |

dc.contributor.author | Irina Krop | |

dc.date.accessioned | 2024-05-21T13:41:13Z | |

dc.date.available | 2024-05-21T13:41:13Z | |

dc.description.abstract | Let $f(n,p,q)$ be the minimum number of colors necessary to color the edges of $K_n$ so that every $K_p$ is at least $q$-colored. We improve current bounds on these nearly ``anti-Ramsey" numbers, first studied by Erd\H os and Gy\'arf\'as. We show that $f(n,5,9) \geq \frac{7}{4}n-3$, slightly improving the bound of Axenovich. We make small improvements on bounds of Erd\H os and Gy\'arf\'as by showing $\frac{5}{6}n+1\leq f(n,4,5)$ and for all even $n\not\equiv 1 \pmod 3$, $f(n,4,5)\leq n-1$ . For a complete bipartite graph $G=K_{n,n}$, we show an n-color construction to color the edges of $G$ so that every $C_4\subseteq G$ is colored by at least three colors. This improves the best known upper bound of M. Axenovich, Z. F\"uredi, and D. Mubayi. | |

dc.identifier | oas.uz.zgora.pl:7777/bib/bibwww.bwww_cz_spis?nIdCzasopisma=402&nVol=33&nNr=4 | |

dc.identifier.uri | https://hdl.handle.net/20.500.12951/1016 | |

dc.title | Almost-rainbow edge-colorings of some small subgraphs | |

dc.type | Journal Article, Academic Journal | |

dcterms.bibliographicCitation | Discussiones Mathematicae Graph Theory 33(4), 771-784, (September 2013) |