Summary: We introduce and study the concept of \(F\)-coverable graphs. For two graphs \(F\) and \(G\), we say that \(G\) is \(F\)-coverable if some weights \(f(H)\) can be assigned to the subgraphs \(H\) isomorphic to \(F\) in \(G\) in such a way that \[ 0\leq f(H)\leq 1\quad\text{and} \quad \sum_{e\in H\subset G} f(H)= 1 \] holds for every edge \(e\) of \(G\). We concentrate on the case where \(F\) is the complete graph on three vertices. We prove necessary conditions, reduction theorems, and non-existence results concerning \(K_3\)-coverable graphs. Our theorems can be applied in the theory of triple systems with index \(\lambda> 1\), and further applications are expected in design theory.