Flip colouring of graphs II

We give results concerning two problems on the recently introduced flipcolourings of graphs, a new class of local v. global phenomena. We prove thatfor $(b, r)$-flip sequences with $4 \leq b < r < b + 2\left\lfloor\frac{b+2}{6}\right\rfloor^2$, small constructions of $(b,r)$-flipgraphs on $O(b+r)$ vertices are possible. Furthermore, we prove that thereexists $k$-flip sequences $(a_1, \dots, a_k)$ where $k > 4$, such that $a_k$can be arbitrarily large whilst $a_i$ is constant for $1 \leq i < \frac{k}{4}$.