On the ascending subgraph decomposition problem for bipartite graphs

The Ascending Subgraph Decomposition (ASD) Conjecture asserts that every graph G with edges admits an edge decomposition G=H1⊕⋯⊕Hn such that Hi has i edges and is isomorphic to a subgraph of Hi+1, i=1,…,n−1. We show that every bipartite graph G with edges such that the degree sequence d1,…,dk of one of the stable sets satisfies di≥n−i+2, 1≤i