Radial Level Planarity with Fixed Embedding

We study level planarity testing of graphs with a fixed combinatorial embedding for three different notions embeddings, namely the embedding, upward and planar embedding. These allow increasing degrees freedom in their corresponding drawings. For there are known easy to test criteria. use these criteria prove an untangling lemma that plays key role simple case where only is fixed. This then adapted Further, we characterize radial which lets us extend our results planarity. No algorithms were previously problems.