2026-04-17T05:15:22Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/1123252025-07-17T10:24:38Zcom_2072_1033col_2072_452950

On star forest ascending subgraph decomposition Aroca Farrerons, José María Lladó Sánchez, Ana M. Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria Graph theory Ascending graph decomposition Grafs, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory 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. Peer Reviewed Postprint (author's final draft) 2017-02-03 Article http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i1p14 http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Open Access Attribution-NonCommercial-NoDerivs 3.0 Spain