Robust cycle bases do not exist for Kn,n if n≥8

A basis for the cycle space of a graph is said to be robust if any cycle Z of G is a sum Z=C1+C2+⋯+Ck of basis elements such that (i) (C1+C2+⋯+Cℓ−1)∩Cℓ is a nontrivial path for each 2≤ℓ