Fully Dynamic Recognition of Proper Circular-Arc Graphs

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We present a fully dynamic algorithm for the recognition of proper circular-arc (PCA) graphs. The allowed operations on the graph involve the insertion and removal of vertices (together with its incident edges) or edges. Edge operations cost O(logn) time, where n is the number of vertices of the gra...

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Autor principal:	Soulignac, Francisco Juan
Publicado:	2015
Materias:	Co-connectivity Dynamic recognition Minimal forbidden induced subgraphs Proper circular-arc graphs Round graphs Algorithms Graphic methods Connectivity algorithms Decremental algorithms Forbidden induced subgraphs Fully dynamic algorithms Induced subgraphs Graph theory
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01784617_v71_n4_p904_Soulignac http://hdl.handle.net/20.500.12110/paper_01784617_v71_n4_p904_Soulignac
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_01784617_v71_n4_p904_Soulignac
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spelling	paper:paper_01784617_v71_n4_p904_Soulignac2023-06-08T15:19:17Z Fully Dynamic Recognition of Proper Circular-Arc Graphs Soulignac, Francisco Juan Co-connectivity Dynamic recognition Minimal forbidden induced subgraphs Proper circular-arc graphs Round graphs Algorithms Graphic methods Connectivity algorithms Decremental algorithms Dynamic recognition Forbidden induced subgraphs Fully dynamic algorithms Induced subgraphs Proper circular-arc graphs Round graphs Graph theory We present a fully dynamic algorithm for the recognition of proper circular-arc (PCA) graphs. The allowed operations on the graph involve the insertion and removal of vertices (together with its incident edges) or edges. Edge operations cost O(logn) time, where n is the number of vertices of the graph, while vertex operations cost O(logn+d) time, where d is the degree of the modified vertex. We also show incremental and decremental algorithms that work in O(1) time per inserted or removed edge. As part of our algorithm, fully dynamic connectivity and co-connectivity algorithms that work in O(logn) time per operation are obtained. Also, an O(Δ) time algorithm for determining if a PCA representation corresponds to a co-bipartite graph is provided, where Δ is the maximum among the degrees of the vertices. When the graph is co-bipartite, a co-bipartition of each of its co-components is obtained within the same amount of time. As an application, we show how to find a minimal forbidden induced subgraph of a static graph in O(n+m) time. © 2013, Springer Science+Business Media New York. Fil:Soulignac, F.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2015 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01784617_v71_n4_p904_Soulignac http://hdl.handle.net/20.500.12110/paper_01784617_v71_n4_p904_Soulignac
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Co-connectivity Dynamic recognition Minimal forbidden induced subgraphs Proper circular-arc graphs Round graphs Algorithms Graphic methods Connectivity algorithms Decremental algorithms Dynamic recognition Forbidden induced subgraphs Fully dynamic algorithms Induced subgraphs Proper circular-arc graphs Round graphs Graph theory
spellingShingle	Co-connectivity Dynamic recognition Minimal forbidden induced subgraphs Proper circular-arc graphs Round graphs Algorithms Graphic methods Connectivity algorithms Decremental algorithms Dynamic recognition Forbidden induced subgraphs Fully dynamic algorithms Induced subgraphs Proper circular-arc graphs Round graphs Graph theory Soulignac, Francisco Juan Fully Dynamic Recognition of Proper Circular-Arc Graphs
topic_facet	Co-connectivity Dynamic recognition Minimal forbidden induced subgraphs Proper circular-arc graphs Round graphs Algorithms Graphic methods Connectivity algorithms Decremental algorithms Dynamic recognition Forbidden induced subgraphs Fully dynamic algorithms Induced subgraphs Proper circular-arc graphs Round graphs Graph theory
description	We present a fully dynamic algorithm for the recognition of proper circular-arc (PCA) graphs. The allowed operations on the graph involve the insertion and removal of vertices (together with its incident edges) or edges. Edge operations cost O(logn) time, where n is the number of vertices of the graph, while vertex operations cost O(logn+d) time, where d is the degree of the modified vertex. We also show incremental and decremental algorithms that work in O(1) time per inserted or removed edge. As part of our algorithm, fully dynamic connectivity and co-connectivity algorithms that work in O(logn) time per operation are obtained. Also, an O(Δ) time algorithm for determining if a PCA representation corresponds to a co-bipartite graph is provided, where Δ is the maximum among the degrees of the vertices. When the graph is co-bipartite, a co-bipartition of each of its co-components is obtained within the same amount of time. As an application, we show how to find a minimal forbidden induced subgraph of a static graph in O(n+m) time. © 2013, Springer Science+Business Media New York.
author	Soulignac, Francisco Juan
author_facet	Soulignac, Francisco Juan
author_sort	Soulignac, Francisco Juan
title	Fully Dynamic Recognition of Proper Circular-Arc Graphs
title_short	Fully Dynamic Recognition of Proper Circular-Arc Graphs
title_full	Fully Dynamic Recognition of Proper Circular-Arc Graphs
title_fullStr	Fully Dynamic Recognition of Proper Circular-Arc Graphs
title_full_unstemmed	Fully Dynamic Recognition of Proper Circular-Arc Graphs
title_sort	fully dynamic recognition of proper circular-arc graphs
publishDate	2015
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01784617_v71_n4_p904_Soulignac http://hdl.handle.net/20.500.12110/paper_01784617_v71_n4_p904_Soulignac
work_keys_str_mv	AT soulignacfranciscojuan fullydynamicrecognitionofpropercirculararcgraphs
_version_	1768544637724655616

Fully Dynamic Recognition of Proper Circular-Arc Graphs

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