On star forest ascending subgraph decomposition

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 sequen...

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Detalles Bibliográficos
Autores: Aroca Farrerons, José María|||0000-0002-5807-653X, Lladó Sánchez, Ana M.|||0000-0002-0993-6556
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/112325
Acceso en línea:https://hdl.handle.net/2117/112325
Access Level:acceso abierto
Palabra clave:Graph theory
Ascending graph decomposition
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
Descripción
Sumario: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.