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Constructing the spectrum for packings of the complete graph with trees that have up to five edges. (English) Zbl 1355.05196
For graphs \(G\) and \(H\), a \(G\)-packing of \(H\) is a collection of subgraphs of \(H\), each isomorphic to \(G\), such that every edge of \(H\) is contained in at most one subgraph. Those edges of \(H\) which are not included in any of the subgraphs form the leave graph. A maximum \(G\)-packing of \(H\) is a packing with the smallest number of edges in the leave graph.
The spectrum problem for packing for a graph \(G\) is the problem of obtaining all possible leave graphs for \(G\)-packings of a complete graph \(K_n\). Here, the authors solve the spectrum problem for packing for all trees with up to five edges.

05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C05 Trees