The anti-Ramsey threshold of complete graphs
نویسندگان
چکیده
For graphs G and H, let G?rbH denote the property that, for every proper edge-colouring of G, there is a rainbow H in G. graph threshold function pHrb=pHrb(n) this random G(n,p) satisfies pHrb=O(n?1/m(2)(H)), where m(2)(H) denotes so-called maximum 2-density H. Completing result Nenadov, Person, Škori?, Steger [J. Combin. Theory Ser. B 124 (2017), 1–38], we prove matching lower bound pKkrb k?5. Furthermore, show that pK4rb=n?7/15?n?1/m(2)(K4).
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2023
ISSN: ['1872-681X', '0012-365X']
DOI: https://doi.org/10.1016/j.disc.2023.113343