Past exam of the computer science course of the University of Oxford / 2023 / Artificial intelligence / 3 / d / Solution

Before using no-waste allocation to restrict the constraint domains, there is one constraint graph vertex for each of $A,B,C,D,E$. Every distinct pair has a disjointness binary constraint, and also the two directional envy-free allocation constraints. Thus the constraint graph is the complete graph $K_5$, with all ten edges.

The nonempty-bundle and no-waste allocation requirements are unary and add no edges. The original all-item coverage constraint has been removed because this variant permits unallocated items.