Packing bipartite graphs

AbstractFor two bipartite graphs G = (L, R; E) and G′ = (L′, R′; E′) a bijection ƒ : L∪R → L′∪ R′ such that ƒ (L) = L′ is called bi-placement when ƒ (u) ƒ (v)∉ E′, for every edge uv ∈ E (then G and G′ are called bi-placeable).We give new sufficient conditions for bipartite graphs G and G′ to be bi-placeable. When ΔR(G) = ΔR(G′) = 1 (i.e. when all vertices of R and R′ are pendent or isolated), we prove a necessary and sufficient condition for G and G′ to be bi-placeable