March 2018 Detroit Mercy Math Problem

Send solutions to by April 30, 2018 (extended deadline).

The arrangement graph \(A_{n,k}\) (with \(n>k\geq 1\)) has a vertex set consisting of all possible permutations of \(k\) elements chosen from the ground set of \(n\) elements \(\{1,2,\ldots , n\}\). Two vertices (nodes) \(u\) and \(v\) of \(A_{n,k}\) are adjacent if their corresponding permutations differ in exactly one of the \(k\) positions.

A hamiltonian cycle in a graph is a closed path through a graph that visits each node exactly once.

And here is the March 2018 problem (PDF)

Find three edge disjoint hamiltonian cycles in \(A_{5,2}\) shown below.

The special pentagon
Figure 1: The graph \(A_{5,2}\) contains three edge disjoint hamiltonian cycles.

Selected best solutions submitted by April 30, 2018 will be posted here!

A hint for March 2018 Problem

Back to the Detroit Mercy Math Competition page.
Older web puzzles page.