Narrow tubeless tire on wide rim A recent trend toward wider tires (cf Heine, "Performance of Tires") also led to wider rims and a closer match of rim and tire widths.

In the past it was considered that tires need to be considerably wider than their rims. For example, Sheldon Brown requires at least 40 mm nominal width in a 23 mm rim (measure between inner flanges). ISO 4210 (cf Mavic) requires at least a 37 mm tire on the same rim.

As a recent example, my new bike (2017 Merida CX 600) came with a 700x23C rim and 32-622 tires. This choice of the manufacturer suggests it is a safe combination. The rim lacks hooks though (see below), which might make it comparable to a narrower specification.

New developments, such as tubeless, hook-less rims, and tubeless tire beads made this question more complicated then it was a decade ago. This merritts to discuss this beyond Brown and ISO 4210. 

What is the smallest width a tubeless tire may have to be mounted on a rim of given width?
I was googling a similar thing and stumbled across both this question, and an interesting article from mavic:
https://engineerstalk.mavic.com/en/the-right-tyre-width-on-the-right-rim-width/

Towards the bottom of the article are some interesting tables for not only tyre size vs rim width (internal) but also pressure: