Geodesic
Packing Trees in Complete Bipartite Graphs
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 1, pp. 263-275

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An embedding of a graph H in a graph G is an injection (i.e., a one-to-one function) σ from the vertices of H to the vertices of G such that σ(x)σ(y) is an edge of G for all edges xy of H. The image of H in G under σ is denoted by σ(H). A k-packing of a graph H in a graph G is a sequence (σ1, σ2,…, σk) of embeddings of H in G such that σ1(H), σ2(H),…, σk(H) are edge disjoint. We prove that for any tree T of order n, there is a 4-packing of T in a complete bipartite graph of order at most n+12.
Keywords: packing, placement, edge-disjoint tree, bipartite graph 
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Wang, Jieyan. Packing Trees in Complete Bipartite Graphs. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 1, pp. 263-275. http://geodesic.mathdoc.fr/item/DMGT_2022_42_1_a16/