[Phemist]

so in essence there is an additional constraint, that each touching edge has to be of a given minimal size. Each contiguous "blob" with a given circumference of N * this minimal size, can only connect to at most N other blobs.

[ColinWright]

No, there is no minimal size, just that we only consider two regions as being "in contact" and therefore requiring different colours) if they have a shared boundary, and that boundary is of non-zero length.

There is no limit to how many regions can surround and be in contact with a given region, it's just that the shared border that defines "in contact with" must be of non-zero length.

Note also: we are dealing with finite maps. That means that for any given map there will be a shortest boundary for that map, but it doesn't mean there is a minimum constraint.