I'm trying to prove that the Subgraph isomorphism problem is NPC using the Hamiltonian Cycle problem.
Unfortunately I feel (or don't understand) that the solution is "empty" and doesn't explain the Hamiltonian Cycle - Subgraph Isomorphic connection, @Luke Mathieson says that "Hamiltonian Cycle to Subgraph Isomorphism is really just rephrasing what it means for a graph to have a Hamiltonian cycle" - but I don't get it.
How does one transforms from Hamiltonian Cycle to Subgraph Isomorphism?
I read Reducing from Hamiltonian Cycle to Subgraph Isomorphism and https://en.wikipedia.org/wiki/Subgraph_isomorphism_problem and couldn't understand how should a proper reduction look like, how to build one that proves the subgraph problem?
Your help in simplifying the problem(s) will be very appreciated.