The 3-Coloring decision problem is "Given a graph G, does G have a 3-coloring?" The 4-Coloring decision problem is "Given a graph G, does G have a 4-coloring?"
The Knapsack Problem is defined as follows. The input is a list of item values v_{1},...,v_{n}, item weights w_{1},...,w_{n}, a target value V, and a maximum capacity W. The decision problem is "Does there exist a subset S of {1,...,n} for which ∑_{i ∈ S} v_{i} ≥ V, and ∑_{i ∈ S} w_{i} ≤ W?"