Abstract: A decomposition of a graph G is a collection of graphs H_1,…,H_m such that G is an edge-disjoint union of H_1,…,H_m.
We say that G has an ascending subgraph decomposition if there exists a decomposition of G such that e(H_i) = i, and each H_i is isomorphic to a subgraph of H_{i+1}. A necessary conditi