A Hamilton Path visits every vertice once

A Hamilton Tour visits every vertice once (and comes back to itself)

An Euler Path visits every edge once and it has exactly two vertices of odd degree

An Euler Tour visits every edge once and all of its vertices are of even degree!

// reminder: tractable - polynomial time / intracatable - exponential time

• tractable: can we find a simple path connecting two vertices in a graph?
tractable: what’s the shortest such path?
intractable: what’s the longest such path?

• tractable: is there a clique in a given graph?
intractable: what’s the largest clique?

• tractable: given two colours, can we colour every vertex in a graph
such that no two adjacent vertices are the same colour?
intractable: what about three colours?