Flip colouring of graphs II

We give results concerning two problems on the recently introduced flip colourings of graphs, a new class of local v. global phenomena. We prove that for (b, r)-flip sequences with 4 ≤ b < r < b + 2 ⌊b+2/6⌋^2, small constructions of (b,r)-flip graphs on O(b+r) vertices are possible. Furthermore, we prove that there exists k-flip sequences (a_1, …, a_k) where k > 4, such that a_k can be arbitrarily large whilst a_i is constant for 1 ≤ i < k/4.