Single Type Only
Different to a monotype run (where all Pokémon on your team need to share a common type, e.g. Bug) - a Single Type Only run is where each of your Pokémon can only have one type.
This can seriously limit the Pokémon available to you and therefore, if you plan on sticking to the 'first eligible Pokémon found on the route' approach, players may want to introduce a '3 lives' rule due to the lack of available Pokémon.
For example, in a Gen 1 run, some of the available Pokémon are: Charmeleon (but not Charizard due to gaining the flying type), Blastoise, Arbok, Raichu and Sandslash.