Mutual placement of bipartite graphs

Fouquet, J.-L. and A.P. Wojda, Mutual placement of bipartite graphs, Discrete Mathematics 121 (1993) 85-92. Let G =(L, R, E) and H =(L’, R’, E’) be bipartite graphs. A bijection 4: L w R + L’v R’ is said to be a biplacement of G and H if 4(L)= L’ and ~$(x)~$(y)gE’ f or every edge xy of G. A biplacement of G and its copy is called a 2-placement of G. We prove that, with some exceptions, every bipartite graph G of order n and size at most n 2 has a 2-placement. We also give some sufficient conditions for bipartite graphs G and H to have a biplacement.