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 
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/
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[1] D. Burns and S. Schuster, Embedding (p, p−1)-graphs in their complements, Israel J. Math. 30 (1978) 313–320. https://doi.org/10.1007/BF02761996

[2] A. Gyárfás and J. Lehel, Packing trees of different order into Kn, Colloq. Math. Soc. János Bolyai 18 (1978) 463–469.

[3] S.P. Haler and H. Wang, Packing four copies of a tree into a complete graph, Australas. J. Combin. 59 (2014) 323–332.

[4] J.M. Harris, J. Hirst and M.J. Mossingho, Combinatorics and Graph Theory (Springer, New York, 2010). https://doi.org/10.1007/978-0-387-79711-3

[5] B. Orchel, 2-placement of (p, q)- trees, Discuss. Math. Graph Theory 23 (2003) 23–26. https://doi.org/10.7151/dmgt.1183

[6] H. Wang and N. Sauer, Packing three copies of a tree into a complete graph, European J. Combin. 14 (1993) 137–142. https://doi.org/10.1006/eujc.1993.1018

[7] H. Wang, Packing two forests into a bipartite graph, J. Graph Theory 23 (1996) 209–213. https://doi.org/10.1002/(SICI)1097-0118(199610)23:2¡209::AID-JGT12¿3.0.CO;2-B

[8] H. Wang, Packing three copies of a tree into a complete bipartite graph, Ann. Comb. 13 (2009) 261–269. https://doi.org/10.1007/s00026-009-0022-0

[9] M. Woźniak, Packing of graphs and permutations—a survey, Discrete Math. 276 (2004) 379–391. https://doi.org/10.1016/S0012-365X(03)00296-6

[10] H.P. Yap, Packing of graphs—a survey, Discrete Math. 72 (1988) 395–404. https://doi.org/10.1016/0012-365X(88)90232-4