Ethernet patch or crossover router to router [closed]

Solution 1:

Most of the ports you'll find today have something called Auto MDI-X.

From https://en.wikipedia.org/wiki/Medium-dependent_interface:

"Auto MDI-X ports on newer network interfaces detect if the connection would require a crossover, and automatically chooses the MDI or MDI-X configuration to properly match the other end of the link."

You don't mention the model(s) of your devices so I can't lookup what you need exactly. Since both routers are (essentially) connected directly to your switch, I wouldn't expect you to need a crossover cable.

In addition all Gig ports have Auto MDI-X as it is part of the specification. You do, however, mention 'fast Ethernet' and that would signify a 100Mbit switch. Auto MDI-X on that is optional.