# zbMATH — the first resource for mathematics

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.

##### MSC:
 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C05 Trees
##### Keywords:
packing; leave graph; complete graph