讲座内容：

Let G={ G_1, G_2, ..., G_m } be an n-graph system on the same vertex set V, and F be a simple graph with e(F) < m. If there is an injection f: from E(F) to  [m] such that e belongs E(G_{f(e)}) for each e in  E(F), then F is called a partial transversal of G. If e(F) = m, then it is called a transversal of G. We also say that F is a path/cycle/ triangle/ matching (partial) transversal if F is both a transversal and a path/cycle/ triangle/matching. Since all edges of F belong to distinct graphs of G, we also call F a rainbow subgraph of G. In this talk, we will survey some know results on rainbow subgraphs of graph systems. Some unsolved problems are also presented for further study.