I have the following problem.
Given a finite number of lists of items. The same item can appear in many lists. I would like to color items with 3 colors, such at least two colors appear in each list.
I would like to show that this problem is NP-hard. I would like to provide reduction from the 3-coloring problem which seems to be similar.
I think I could make items as nodes and link every item with every other from the shared lists, but then the condition of 3-coloring would be too demanding in comparison to my problem. What should I do differently in order to create the reduction?