Abstract
The Ascending Subgraph Decomposition (ASD) Conjecture asserts that every graph G with (n+12) 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 (n+12) edges such that the degree sequence d1,…,dk of one of the stable sets satisfies di≥n−i+2, 1≤i<k, admits an ascending subgraph decomposition with star forests. We also give a necessary condition on the degree sequence which is not far from the above sufficient one.
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