Gyárfás's monochromatic component covering conjecture
Gyárfás's conjecture. For fixed kkk, there exist sets A1,A2,…,Ak−1A_1,A_2,\dots,A_{k-1}A1,A2,…,Ak−1 whose union is [n][n][n], and colours c1,c2,…,ck−1c_1,c_2,\dots,c_{k-1}c1,c2,…,ck−1, such that Kn[Ai,ci]K_n[A_i,c_i]Kn[Ai,ci] is connected for e…