On characterizing proper max-point-tolerance graphs
AbstractMax-point-tolerance graphs (MPTG) were introduced by Catanzaro et al. in 2017 as a generalization of interval graphs. This graph class has many practical applications in the study of the human genome as well as in signal processing for networks. The same class of graphs was also studied by S...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2023-09-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2023.2245430 |
| _version_ | 1797385628662366208 |
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| author | Sanchita Paul |
| author_facet | Sanchita Paul |
| author_sort | Sanchita Paul |
| collection | DOAJ |
| description | AbstractMax-point-tolerance graphs (MPTG) were introduced by Catanzaro et al. in 2017 as a generalization of interval graphs. This graph class has many practical applications in the study of the human genome as well as in signal processing for networks. The same class of graphs was also studied by Soto and Caro in 2015 with a different name, p -BOX(1) graphs. In our article, we consider a natural subclass of max-point-tolerance graphs, namely, proper max-point-tolerance graphs (proper MPTG), where intervals associated with the vertices are not contained in each other properly. We present the first characterization theorem of this graph class by defining certain linear ordering on the vertex set. In the course of this study, we prove proper max-point-tolerance graphs are asteroidal triple-free, and perfect. We also find that proper max-point-tolerance graphs are equivalent to unit max-point-tolerance graphs. Further, we show that MPTG (proper MPTG) and max-tolerance graphs (proper max-tolerance graphs) are incomparable. In conclusion, we demonstrate relations between proper MPTG with other variants of MPTG and max-tolerance graphs. |
| first_indexed | 2024-03-08T21:56:55Z |
| format | Article |
| id | doaj.art-59a417ada8d345bbb393170816dc0a46 |
| institution | Directory Open Access Journal |
| issn | 0972-8600 2543-3474 |
| language | English |
| last_indexed | 2024-03-08T21:56:55Z |
| publishDate | 2023-09-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-59a417ada8d345bbb393170816dc0a462023-12-19T17:41:02ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742023-09-0120331332510.1080/09728600.2023.2245430On characterizing proper max-point-tolerance graphsSanchita Paul0Department of Mathematics, Jadavpur University, Kolkata, IndiaAbstractMax-point-tolerance graphs (MPTG) were introduced by Catanzaro et al. in 2017 as a generalization of interval graphs. This graph class has many practical applications in the study of the human genome as well as in signal processing for networks. The same class of graphs was also studied by Soto and Caro in 2015 with a different name, p -BOX(1) graphs. In our article, we consider a natural subclass of max-point-tolerance graphs, namely, proper max-point-tolerance graphs (proper MPTG), where intervals associated with the vertices are not contained in each other properly. We present the first characterization theorem of this graph class by defining certain linear ordering on the vertex set. In the course of this study, we prove proper max-point-tolerance graphs are asteroidal triple-free, and perfect. We also find that proper max-point-tolerance graphs are equivalent to unit max-point-tolerance graphs. Further, we show that MPTG (proper MPTG) and max-tolerance graphs (proper max-tolerance graphs) are incomparable. In conclusion, we demonstrate relations between proper MPTG with other variants of MPTG and max-tolerance graphs.https://www.tandfonline.com/doi/10.1080/09728600.2023.2245430Interval graphproper interval graphtolerance graphmax-tolerance graphmax-point-tolerance graph05C62 |
| spellingShingle | Sanchita Paul On characterizing proper max-point-tolerance graphs AKCE International Journal of Graphs and Combinatorics Interval graph proper interval graph tolerance graph max-tolerance graph max-point-tolerance graph 05C62 |
| title | On characterizing proper max-point-tolerance graphs |
| title_full | On characterizing proper max-point-tolerance graphs |
| title_fullStr | On characterizing proper max-point-tolerance graphs |
| title_full_unstemmed | On characterizing proper max-point-tolerance graphs |
| title_short | On characterizing proper max-point-tolerance graphs |
| title_sort | on characterizing proper max point tolerance graphs |
| topic | Interval graph proper interval graph tolerance graph max-tolerance graph max-point-tolerance graph 05C62 |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2023.2245430 |
| work_keys_str_mv | AT sanchitapaul oncharacterizingpropermaxpointtolerancegraphs |