Guichard-Combinatorics-Graph-Theory · Problem 4.1.1

A system of distinct representatives (SDR) picks one element from each set such that all choices are different. Here, the sets form a cycle where $A_i$ contains $i$ and $i+1$ (mod $n$), so you're essentially assigning each position a value while respecting the constraint that adjacent sets share an element. The key insight is to think of this as a matching problem: which elements can you pick from each set without repetition, and how does the cyclic structure force your choices?

A system of distinct representatives (SDR) picks one element from each set such that all choices are different. Here, the sets form a cycle where $A_i$ contains $i$ and $i+1$ (mod $n$), so you're essentially assigning each position a value while respecting the constraint that adjacent sets share an element. The key insight is to think of this as a matching problem: which elements can you pick from each set without repetition, and how does the cyclic structure force your choices?