On the thinness and proper thinness of a graph

Graphs with bounded thinness were defined in 2007 as a generalization of interval graphs. In this paper we introduce the concept of proper thinness, such that graphs with bounded proper thinness generalize proper interval graphs. We study the complexity of problems related to the computation of thes...

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Detalles Bibliográficos
Autores principales:	Bonomo, F., de Estrada, D.
Formato:	INPR
Materias:	Interval graphs Proper interval graphs Proper thinness Thinness
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_0166218X_v_n_p_Bonomo
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_0166218X_v_n_p_Bonomo2023-10-03T15:03:47Z On the thinness and proper thinness of a graph Bonomo, F. de Estrada, D. Interval graphs Proper interval graphs Proper thinness Thinness Graphs with bounded thinness were defined in 2007 as a generalization of interval graphs. In this paper we introduce the concept of proper thinness, such that graphs with bounded proper thinness generalize proper interval graphs. We study the complexity of problems related to the computation of these parameters, describe the behavior of the thinness and proper thinness under three graph operations, and relate thinness and proper thinness to other graph invariants in the literature. Finally, we describe a wide family of problems that can be solved in polynomial time for graphs with bounded thinness, generalizing for example list matrix partition problems with bounded size matrix, and enlarge this family of problems for graphs with bounded proper thinness, including domination problems. © 2018 Elsevier B.V. INPR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0166218X_v_n_p_Bonomo
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Interval graphs Proper interval graphs Proper thinness Thinness
spellingShingle	Interval graphs Proper interval graphs Proper thinness Thinness Bonomo, F. de Estrada, D. On the thinness and proper thinness of a graph
topic_facet	Interval graphs Proper interval graphs Proper thinness Thinness
description	Graphs with bounded thinness were defined in 2007 as a generalization of interval graphs. In this paper we introduce the concept of proper thinness, such that graphs with bounded proper thinness generalize proper interval graphs. We study the complexity of problems related to the computation of these parameters, describe the behavior of the thinness and proper thinness under three graph operations, and relate thinness and proper thinness to other graph invariants in the literature. Finally, we describe a wide family of problems that can be solved in polynomial time for graphs with bounded thinness, generalizing for example list matrix partition problems with bounded size matrix, and enlarge this family of problems for graphs with bounded proper thinness, including domination problems. © 2018 Elsevier B.V.
format	INPR
author	Bonomo, F. de Estrada, D.
author_facet	Bonomo, F. de Estrada, D.
author_sort	Bonomo, F.
title	On the thinness and proper thinness of a graph
title_short	On the thinness and proper thinness of a graph
title_full	On the thinness and proper thinness of a graph
title_fullStr	On the thinness and proper thinness of a graph
title_full_unstemmed	On the thinness and proper thinness of a graph
title_sort	on the thinness and proper thinness of a graph
url	http://hdl.handle.net/20.500.12110/paper_0166218X_v_n_p_Bonomo
work_keys_str_mv	AT bonomof onthethinnessandproperthinnessofagraph AT deestradad onthethinnessandproperthinnessofagraph
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On the thinness and proper thinness of a graph

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