You can wash your hair the day after but it is best to allow the cuticle of the hair to close up as much as it can naturally. I purposely color my hair on Friday so I can have the weekend so I don't need to be anywhere to wash it.
Coloring and perming completely blow open the cuticle the hair and coloring deposits color into the cortex. It does take a few days to close more naturally and if washed before that you have a greater chance of losing color. Of course lots of people wash right away and everyones hair is different and some people have hair where color loss is nil or minimal.
Darker colors or reds are more apt for color loss because their color molecules are larger.
I always use either Joico KPAK 24-36 hours before a treatment or ApHogee two step protein treatment before a treatment. These treatments fill in (with protein) any porous, damaged hair and even it out from root to tip and are bonded into the hair with heat. That way when you wash after a chemical process you get less damage and unevenness and damage causes color loss. I used these two products on all my color clients especially if they had uneven porosity.
Those who make peaceful revolution impossible will make violent revolution inevitable.
JFK