On star forest ascending subgraph decomposition
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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 it 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 dk-i=n-ifor each0=i=k-1, 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.
CitationAroca, J., Llado, A. On star forest ascending subgraph decomposition. "Electronic journal of combinatorics", 3 Febrer 2017, vol. 24, núm. 1, p. 1-12.