On Nontrivial Covers and Partitions of Graphs by Convex Sets

In this paper we prove that it is NP-complete to decide whether a graph can be partitioned into nontrivial convex sets. We show that it can be verified in polynomial time whether a graph can be covered by nontrivial convex sets. Also, we propose a recursive formula that establishes the maximum nontr...

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Main Authors:	Radu Buzatu, Sergiu Cataranciuc
Format:	Article
Language:	English
Published:	Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova 2018-05-01
Series:	Computer Science Journal of Moldova
Subjects:	Convexity complexity nontrivial convex cover nontrivial convex partition tree
Online Access:	http://www.math.md/files/csjm/v26-n1/v26-n1-(pp3-14).pdf

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spelling	doaj-776c53224ac349c1b12f85bf3059dc082020-11-24T23:37:59ZengInstitute of Mathematics and Computer Science of the Academy of Sciences of MoldovaComputer Science Journal of Moldova1561-40422018-05-01261(76)314On Nontrivial Covers and Partitions of Graphs by Convex SetsRadu Buzatu0Sergiu Cataranciuc1State University of Moldova, 60 A. Mateevici, MD-2009, Chisinau, Republic of MoldovaState University of Moldova, 60 A. Mateevici, MD-2009, Chisinau, Republic of MoldovaIn this paper we prove that it is NP-complete to decide whether a graph can be partitioned into nontrivial convex sets. We show that it can be verified in polynomial time whether a graph can be covered by nontrivial convex sets. Also, we propose a recursive formula that establishes the maximum nontrivial convex cover number of a tree.http://www.math.md/files/csjm/v26-n1/v26-n1-(pp3-14).pdfConvexitycomplexitynontrivial convex covernontrivial convex partitiontree
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Radu Buzatu Sergiu Cataranciuc
spellingShingle	Radu Buzatu Sergiu Cataranciuc On Nontrivial Covers and Partitions of Graphs by Convex Sets Computer Science Journal of Moldova Convexity complexity nontrivial convex cover nontrivial convex partition tree
author_facet	Radu Buzatu Sergiu Cataranciuc
author_sort	Radu Buzatu
title	On Nontrivial Covers and Partitions of Graphs by Convex Sets
title_short	On Nontrivial Covers and Partitions of Graphs by Convex Sets
title_full	On Nontrivial Covers and Partitions of Graphs by Convex Sets
title_fullStr	On Nontrivial Covers and Partitions of Graphs by Convex Sets
title_full_unstemmed	On Nontrivial Covers and Partitions of Graphs by Convex Sets
title_sort	on nontrivial covers and partitions of graphs by convex sets
publisher	Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova
series	Computer Science Journal of Moldova
issn	1561-4042
publishDate	2018-05-01
description	In this paper we prove that it is NP-complete to decide whether a graph can be partitioned into nontrivial convex sets. We show that it can be verified in polynomial time whether a graph can be covered by nontrivial convex sets. Also, we propose a recursive formula that establishes the maximum nontrivial convex cover number of a tree.
topic	Convexity complexity nontrivial convex cover nontrivial convex partition tree
url	http://www.math.md/files/csjm/v26-n1/v26-n1-(pp3-14).pdf
work_keys_str_mv	AT radubuzatu onnontrivialcoversandpartitionsofgraphsbyconvexsets AT sergiucataranciuc onnontrivialcoversandpartitionsofgraphsbyconvexsets
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On Nontrivial Covers and Partitions of Graphs by Convex Sets

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