Dominating sets and local treewidth

It is known that the treewidth of a planar graph with a dominating set of size d is O(sqrt{d}) and this fact is used as the basis for several fixed parameter algorithms on planar graphs. An interesting question motivating our study is if similar bounds can be obtained for larger minor closed graph f...

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Detalles Bibliográficos
Autores: Thilikos Touloupas, Dimitrios, Fomin, Fedor V.
Tipo de recurso: informe técnico
Fecha de publicación:2003
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:2117/96914
Acceso en línea:https://hdl.handle.net/2117/96914
Access Level:acceso abierto
Palabra clave:Planar graphs
Dominating sets
Local treewidth
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
Descripción
Sumario:It is known that the treewidth of a planar graph with a dominating set of size d is O(sqrt{d}) and this fact is used as the basis for several fixed parameter algorithms on planar graphs. An interesting question motivating our study is if similar bounds can be obtained for larger minor closed graph families. We say that a graph family F has the {domination-treewidth property} if there is some function f(d) such that every graph G in F with dominating set of size at most d has treewidth at most f(d). We show that a minor-closed graph family F has the domination-treewidth property if and only if F has bounded local treewidth. This result has important algorithmic consequences.