Complexity of Higher-Degree Orthogonal Graph Embedding in the Kandinsky   Model
  We show that finding orthogonal grid-embeddings of plane graphs (planar with fixed combinatorial embedding) with the minimum number of bends in the so-called Kandinsky model (which allows vertices of degree $> 4$) is NP-complete, thus solving a long-standing open problem. On the positive side, we give an efficient algorithm for several restricted variants, such as graphs of bounded branch width and a subexponential exact algorithm for general plane graphs. 
Thomas Bl\"asius and Guido Br\"uckner and Ignaz Rutter
cs.CG cs.DS