Packing Trees into 1-planar Graphs

We introduce and study the 1-planar packing problem: Given k graphs with n vertices \(G_1, \dots , G_k\), find a graph that contains given as edge-disjoint spanning subgraphs. mainly focus on case when each \(G_i\) is tree \(k=3\). prove triple consisting of three caterpillars or two path may not admit packing, while paths special type caterpillar always have one. then packings few crossings (resp. cycles) at most seven fourteen) crossings. finally show quadruple perfect matching \(n \ge 12\) admits such does exist if \le 10\).