Mutual-visibility in distance-hereditary graphs: a linear-time algorithm
The concept of mutual-visibility in graphs has been recently introduced. If X is a subset of vertices of a graph G, then vertices u and v are X-visible if there exists a shortest u, v-path P such that V(P) ∩ X⊆ {u, v}. If every two vertices from X are X-visible, then X is a mutual-visibility set. Th...
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| Vydané v: | Procedia computer science Ročník 223; s. 104 - 111 |
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| Jazyk: | English |
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Elsevier B.V
2023
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| ISSN: | 1877-0509, 1877-0509 |
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| Abstract | The concept of mutual-visibility in graphs has been recently introduced. If X is a subset of vertices of a graph G, then vertices u and v are X-visible if there exists a shortest u, v-path P such that V(P) ∩ X⊆ {u, v}. If every two vertices from X are X-visible, then X is a mutual-visibility set. The mutual-visibility number of G is the cardinality of a largest mutual-visibility set of G. It is known that computing the mutual-visibility number of a graph is NP-complete, whereas it has been shown that there are exact formulas for special graph classes like paths, cycles, blocks, cographs, and grids. In this paper, we study the mutual-visibility in distance-hereditary graphs and show that the mutual-visibility number can be computed in linear time for this class. |
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| AbstractList | The concept of mutual-visibility in graphs has been recently introduced. If X is a subset of vertices of a graph G, then vertices u and v are X-visible if there exists a shortest u, v-path P such that V(P) ∩ X⊆ {u, v}. If every two vertices from X are X-visible, then X is a mutual-visibility set. The mutual-visibility number of G is the cardinality of a largest mutual-visibility set of G. It is known that computing the mutual-visibility number of a graph is NP-complete, whereas it has been shown that there are exact formulas for special graph classes like paths, cycles, blocks, cographs, and grids. In this paper, we study the mutual-visibility in distance-hereditary graphs and show that the mutual-visibility number can be computed in linear time for this class. |
| Author | Stefano, Gabriele Di Cicerone, Serafino |
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| Cites_doi | 10.1002/jgt.3190120210 10.1093/qmath/28.4.417 10.7717/peerj-cs.627 10.1016/j.ic.2016.09.005 10.1016/S0166-218X(00)00227-4 10.3233/FI-2018-1748 10.2168/LMCS-2(2:2)2006 10.1016/j.tcs.2020.10.033 10.1016/0095-8956(86)90043-2 10.4153/CJM-1980-057-7 10.1016/j.amc.2021.126850 10.1007/978-3-030-11072-7 10.1006/jagm.2000.1090 |
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| Keywords | Mutual visibility Graph classes Graph invariant Computational complexity Graph algorithm |
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| References | Brandstädt, Le, Spinrad (bib0008) 1999 B. Courcelle, The monadic second-order logic of graphs XVI: Canonical graph decompositions, Log. Methods Comput. Sci. 2 (2). doi: 10.2168/LMCS-2(2:2)2006. Cicerone, Di Stefano (bib0007) 2001; 108 Manuel, Klavzar (bib0014) 2018; 163 Poudel, Aljohani, Sharma (bib0012) 2021; 850 Bouchet (bib0009) 1988; 4 Cunningham, Edmonds (bib0015) 1980; 32 P. Flocchini, G. Prencipe, N. Santoro (Eds.), Distributed Computing by Mobile Entities, Current Research in Moving and Computing, Vol. 11340 of LNCS, Springer, 2019. doi:10.1007/978-3-030-11072-7. Cicerone, Di Stefano, Klavžar (bib0002) 2023; 438 Luna, Flocchini, Chaudhuri, Poloni, Santoro, Viglietta (bib0011) 2017; 254 Cicerone, Di Stefano, Klavžar, Yero (bib0003) 2022 Cicerone, Di Stefano (bib0006) 2021; 7 Cicerone, Di Fonso, Di Stefano, Navarra (bib0013) 2023 Di Stefano (bib0001) 2022; 419 Dahlhaus (bib0016) 2000; 36 Bandelt, Mulder (bib0005) 1986; 41 Howorka (bib0004) 1977; 2 Bouchet (10.1016/j.procs.2023.08.219_bib0009) 1988; 4 Cicerone (10.1016/j.procs.2023.08.219_bib0006) 2021; 7 Cunningham (10.1016/j.procs.2023.08.219_bib0015) 1980; 32 Di Stefano (10.1016/j.procs.2023.08.219_bib0001) 2022; 419 Cicerone (10.1016/j.procs.2023.08.219_bib0007) 2001; 108 Poudel (10.1016/j.procs.2023.08.219_bib0012) 2021; 850 10.1016/j.procs.2023.08.219_bib0017 Cicerone (10.1016/j.procs.2023.08.219_bib0002) 2023; 438 Dahlhaus (10.1016/j.procs.2023.08.219_bib0016) 2000; 36 Bandelt (10.1016/j.procs.2023.08.219_bib0005) 1986; 41 Brandstädt (10.1016/j.procs.2023.08.219_bib0008) 1999 10.1016/j.procs.2023.08.219_bib0010 Cicerone (10.1016/j.procs.2023.08.219_bib0013) 2023 Howorka (10.1016/j.procs.2023.08.219_bib0004) 1977; 2 Manuel (10.1016/j.procs.2023.08.219_bib0014) 2018; 163 Cicerone (10.1016/j.procs.2023.08.219_bib0003) 2022 Luna (10.1016/j.procs.2023.08.219_bib0011) 2017; 254 |
| References_xml | – volume: 108 start-page: 3 year: 2001 end-page: 21 ident: bib0007 article-title: Graphs with bounded induced distance publication-title: Discret. Appl. Math. – volume: 438 year: 2023 ident: bib0002 article-title: On the mutual visibility in cartesian products and triangle-free graphs publication-title: Appl. Math. Comput. – start-page: 150 year: 2023 end-page: 159 ident: bib0013 article-title: The geodesic mutual visibility problem for oblivious robots: the case of trees publication-title: 24 – volume: 419 year: 2022 ident: bib0001 article-title: Mutual visibility in graphs publication-title: Applied Mathematics and Computation – volume: 7 start-page: e627 year: 2021 ident: bib0006 article-title: Getting new algorithmic results by extending distance-hereditary graphs via split composition publication-title: PeerJ Comput. Sci. – volume: 850 start-page: 116 year: 2021 end-page: 134 ident: bib0012 article-title: Fault-tolerant complete visibility for asynchronous robots with lights under one-axis agreement publication-title: Theor. Comput. Sci. – volume: 32 start-page: 734 year: 1980 end-page: 765 ident: bib0015 article-title: A combinatorial decomposition theory publication-title: Canadian Journal of Mathematics – volume: 41 start-page: 182 year: 1986 end-page: 208 ident: bib0005 article-title: Distance-hereditary graphs publication-title: J. Comb. Theory Ser. B – volume: 4 start-page: 195 year: 1988 end-page: 207 ident: bib0009 article-title: Transforming trees by successive local complementations publication-title: Journal of Graph Theory – volume: 2 start-page: 417 year: 1977 end-page: 420 ident: bib0004 article-title: A characterization of distance-hereditary graphs publication-title: Quarterly Journal of Mathematics – year: 2022 ident: bib0003 article-title: Mutual-visibility in strong products of graphs via total mutual-visibility publication-title: arXiv: 2210.07835 – year: 1999 ident: bib0008 article-title: Graph classes: a survey – reference: P. Flocchini, G. Prencipe, N. Santoro (Eds.), Distributed Computing by Mobile Entities, Current Research in Moving and Computing, Vol. 11340 of LNCS, Springer, 2019. doi:10.1007/978-3-030-11072-7. – reference: B. Courcelle, The monadic second-order logic of graphs XVI: Canonical graph decompositions, Log. Methods Comput. Sci. 2 (2). doi: 10.2168/LMCS-2(2:2)2006. – volume: 36 start-page: 205 year: 2000 end-page: 240 ident: bib0016 article-title: Parallel algorithms for hierarchical clustering and applications to split decomposition and parity graph recognition publication-title: J. Algorithms – volume: 163 start-page: 339 year: 2018 end-page: 350 ident: bib0014 article-title: The graph theory general position problem on some interconnection networks publication-title: Fundam. Informaticae – volume: 254 start-page: 392 year: 2017 end-page: 418 ident: bib0011 article-title: Mutual visibility by luminous robots without collisions publication-title: Inf. Comput. – volume: 4 start-page: 195 year: 1988 ident: 10.1016/j.procs.2023.08.219_bib0009 article-title: Transforming trees by successive local complementations publication-title: Journal of Graph Theory doi: 10.1002/jgt.3190120210 – volume: 2 start-page: 417 issue: 28 year: 1977 ident: 10.1016/j.procs.2023.08.219_bib0004 article-title: A characterization of distance-hereditary graphs publication-title: Quarterly Journal of Mathematics doi: 10.1093/qmath/28.4.417 – volume: 7 start-page: e627 year: 2021 ident: 10.1016/j.procs.2023.08.219_bib0006 article-title: Getting new algorithmic results by extending distance-hereditary graphs via split composition publication-title: PeerJ Comput. Sci. doi: 10.7717/peerj-cs.627 – volume: 254 start-page: 392 year: 2017 ident: 10.1016/j.procs.2023.08.219_bib0011 article-title: Mutual visibility by luminous robots without collisions publication-title: Inf. Comput. doi: 10.1016/j.ic.2016.09.005 – year: 2022 ident: 10.1016/j.procs.2023.08.219_bib0003 article-title: Mutual-visibility in strong products of graphs via total mutual-visibility publication-title: arXiv: 2210.07835 – volume: 108 start-page: 3 issue: 1-2 year: 2001 ident: 10.1016/j.procs.2023.08.219_bib0007 article-title: Graphs with bounded induced distance publication-title: Discret. Appl. Math. doi: 10.1016/S0166-218X(00)00227-4 – volume: 163 start-page: 339 issue: 4 year: 2018 ident: 10.1016/j.procs.2023.08.219_bib0014 article-title: The graph theory general position problem on some interconnection networks publication-title: Fundam. Informaticae doi: 10.3233/FI-2018-1748 – ident: 10.1016/j.procs.2023.08.219_bib0017 doi: 10.2168/LMCS-2(2:2)2006 – volume: 850 start-page: 116 year: 2021 ident: 10.1016/j.procs.2023.08.219_bib0012 article-title: Fault-tolerant complete visibility for asynchronous robots with lights under one-axis agreement publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2020.10.033 – start-page: 150 year: 2023 ident: 10.1016/j.procs.2023.08.219_bib0013 article-title: The geodesic mutual visibility problem for oblivious robots: the case of trees – volume: 41 start-page: 182 issue: 2 year: 1986 ident: 10.1016/j.procs.2023.08.219_bib0005 article-title: Distance-hereditary graphs publication-title: J. Comb. Theory Ser. B doi: 10.1016/0095-8956(86)90043-2 – volume: 32 start-page: 734 year: 1980 ident: 10.1016/j.procs.2023.08.219_bib0015 article-title: A combinatorial decomposition theory publication-title: Canadian Journal of Mathematics doi: 10.4153/CJM-1980-057-7 – volume: 419 year: 2022 ident: 10.1016/j.procs.2023.08.219_bib0001 article-title: Mutual visibility in graphs publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2021.126850 – volume: 438 year: 2023 ident: 10.1016/j.procs.2023.08.219_bib0002 article-title: On the mutual visibility in cartesian products and triangle-free graphs publication-title: Appl. Math. Comput. – year: 1999 ident: 10.1016/j.procs.2023.08.219_bib0008 – ident: 10.1016/j.procs.2023.08.219_bib0010 doi: 10.1007/978-3-030-11072-7 – volume: 36 start-page: 205 issue: 2 year: 2000 ident: 10.1016/j.procs.2023.08.219_bib0016 article-title: Parallel algorithms for hierarchical clustering and applications to split decomposition and parity graph recognition publication-title: J. Algorithms doi: 10.1006/jagm.2000.1090 |
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| SubjectTerms | Computational complexity Graph algorithm Graph classes Graph invariant Mutual visibility |
| Title | Mutual-visibility in distance-hereditary graphs: a linear-time algorithm |
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