Complexity of finding if a degree bounded graph H is a subgraph of an unbounded graph G You are given two graphs G and H , and want to know if H is a subgraph of G.

You know that H has a max vertex degree K (constant integer).

What can you say about the complexity of this?

I know that 
Isomorphism of Graphs of Bounded Valence Can Be tested in Polynomial Time - Luks 1982,
that's the best I currently have...
If H is the cycle on |G| vertices (and is of maximum degree 2), then this is the Hamiltonian cycle problem. Seems like your problem is NP-hard.