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- Homework Statement
- Show that if a graph G of size m contains a subgraph H of size m' where m' divides m, then G need not be decomposable.

- Homework Equations
- N/A

Can someone please explain H-decomposable graphs. I understand that if all the subgraphs ##H_1, H_2, ..., H_k## are isomorphic to the same graph H, then G is H-decomposable. What I don't understand is, what is H? I'm reading this as there is a subgraph H, that contains a family of subgraphs ##H_1, H_2, ..., H_k##, which doesn't make sense to me. I thought the subgraphs ##H_1, H_2, ..., H_k## were the decomposition of G. Please advise.