Packing smaller graphs into a graph
Let G be a connected graph and \(\alpha_ m(G)\) denote the largest number of vertex-disjoint connected subgraphs \(H_ 1,H_ 2,...,H_ k\) of G each having m vertices. The authors obtain the following bounds for the m-packing number \(\alpha_ m(G)\) for a connected graph G of order n and maximum degree \(\Delta\). \[ \lceil \frac{n-m+1}{(m-1)(\Delta -1)+1}\rceil \leq \alpha_ m(G)\leq \lfloor \frac{n}{m}\rceil. \]
scientific article; zbMATH DE number 4110738