  We present conjectured candidates for the least perimeter partition of a disc
into $N \le 10$ regions which take one of two possible areas. We assume that
the optimal partition is connected, and therefore enumerate all three-connected
simple cubic graphs for each $N$. Candidate structures are obtained by
assigning different areas to the regions: for even $N$ there are $N/2$ regions
of one area and $N/2$ regions of the other, and for odd $N$ we consider both
cases, i.e. where the extra region takes either the larger or the smaller area.
The perimeter of each candidate is found numerically for a few representative
area ratios, and then the data is interpolated to give the conjectured least
perimeter candidate for all possible area ratios. At larger $N$ we find that
these candidates are best for a more limited range of the area ratio.

Soft Condensed Matter