A series of blog posts of 100ish words for Mathober.
By day, $G$ is an ordinary graph. Finite, connected, complete.
When night falls, $G$ dons her extra vertices and edges and becomes … Supergraph!
Are you struggling to cross all the bridges in your town without crossing any of them more than once? Call for Supergraph! She’ll add all the extra edges you need to make your Eulerian path work.
Do you need a way through your graph that visits every vertex exactly once, then returns to the start? Call for Supergraph! She’ll tell you what to do to make your graph Hamiltonian.
Everybody shout ‘Hip, hip, hooray!’ for Supergraph!