Reference: Euler Circuit
Where an
Euler circuit must pass each
link (
edge) exactly once, a Hamiltonian circuit pass go through each
node (
vertex) exactly once. Side note, I learned this week, it's pronounced 'Oil-er', like one who oils, and not 'Euler' like ruler. Please don't sound as ignorant as I did in front of your discrete math professor.
Reference: Hamiltonian Path
While a Hamiltonian path must pass each node exactly once, a Hamiltonian circuit must pass each node exactly once,
and end at the node the path started at. This said,
All Circuits are Paths.
Reference: Traveling Salesman Problem
Commonly referred to as a
TSP, it simulates a salesman who must visit each node preferably once, go home at the end of the day, and have traveled the least distance needed. Any path the salesman takes is a Hamiltonian Circuit.