Place the potatoes in a medium saucepan. Add the salt and enough water to cover the potatoes. Boil the potatoes until they are tender when pierced with the point of a knife but hold their shape (do not overcook), about 30 minutes.
Drain the potatoes, transfer them to a large mixing bowl and allow them to cool completely. Add the hard-boiled eggs, mayonnaise and relish and fold gently to combine. Add salt and pepper to taste. Refrigerate until ready to serve.