2020/10/22 by Liebenau, Anita, Mattos, Letícia, Mendonça, Walner +1
#Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2010.11933
We say that G → (F,H) if, in every edge colouring c: E(G) → \1,2\, we can find either a 1-coloured copy of F or a 2-coloured copy of H. The well-known Kohayakawa--Kreuter conjecture states that the threshold for the property G(n,p) → (F,H) is equal to n^-1/m2(F,H), where m2(F,H) is given by m2(F,H):= max \\dfrace(J)v(J)-2+1/m2(H) : J ⊆ F, e(J)≥ 1 \. In this paper, we show the 0-statement of the Kohayakawa--Kreuter conjecture for every pair of cycles and cliques.