An orientation of an undirected graph G = (V, E) is an assignment of a direction to each edge e E. An acyclic orientation is the assignment of a direction to every edge such that the resulting directed graph contains no cycles. Either prove that there exist undirected graphs with no acyclic orientation, or provide an efficient O(V +E) algorithm for producing an acyclic orientation for an undirected graph G and explain why it produces a valid acyclic orientation.