Transformations among rectangular partitions
We first prove that there always exists a maximal rectangularly dualizable graph for a given rectangularly dualizable graph and present an algorithm for its construction. Further, we show that a maximal rectangularly dualizable graph can always be transformed to an edge-irreducible rectangularly dua...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Isfahan
2023-09-01
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| Series: | Transactions on Combinatorics |
| Subjects: | |
| Online Access: | https://toc.ui.ac.ir/article_26808_fbd1431a1ea5c85b2a6c397dacefc696.pdf |
| _version_ | 1798029279190056960 |
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| author | Vinod Kumar Krishnendra Shekhawat |
| author_facet | Vinod Kumar Krishnendra Shekhawat |
| author_sort | Vinod Kumar |
| collection | DOAJ |
| description | We first prove that there always exists a maximal rectangularly dualizable graph for a given rectangularly dualizable graph and present an algorithm for its construction. Further, we show that a maximal rectangularly dualizable graph can always be transformed to an edge-irreducible rectangularly dualizable graph and present an algorithm that transforms a maximal rectangularly dualizable graph to an edge-irreducible rectangularly dualizable graph. |
| first_indexed | 2024-04-11T19:21:40Z |
| format | Article |
| id | doaj.art-ff6b78bcd6ee4dbea35a277a9f2afb09 |
| institution | Directory Open Access Journal |
| issn | 2251-8657 2251-8665 |
| language | English |
| last_indexed | 2024-04-11T19:21:40Z |
| publishDate | 2023-09-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | Transactions on Combinatorics |
| spelling | doaj.art-ff6b78bcd6ee4dbea35a277a9f2afb092022-12-22T04:07:17ZengUniversity of IsfahanTransactions on Combinatorics2251-86572251-86652023-09-0112314316310.22108/toc.2022.133242.198426808Transformations among rectangular partitionsVinod Kumar0Krishnendra Shekhawat1Department of Mathematics, Birla Institute of Technology and Science, Pilani, Pilani Campus, Rajasthan-333031, IndiaDepartment of Mathematics, Birla Institute of Technology and Science, Pilani, Pilani Campus, Rajasthan-333031, IndiaWe first prove that there always exists a maximal rectangularly dualizable graph for a given rectangularly dualizable graph and present an algorithm for its construction. Further, we show that a maximal rectangularly dualizable graph can always be transformed to an edge-irreducible rectangularly dualizable graph and present an algorithm that transforms a maximal rectangularly dualizable graph to an edge-irreducible rectangularly dualizable graph.https://toc.ui.ac.ir/article_26808_fbd1431a1ea5c85b2a6c397dacefc696.pdfplanar graphrectangular dualrectangularly dualizable graphrectangular partitions |
| spellingShingle | Vinod Kumar Krishnendra Shekhawat Transformations among rectangular partitions Transactions on Combinatorics planar graph rectangular dual rectangularly dualizable graph rectangular partitions |
| title | Transformations among rectangular partitions |
| title_full | Transformations among rectangular partitions |
| title_fullStr | Transformations among rectangular partitions |
| title_full_unstemmed | Transformations among rectangular partitions |
| title_short | Transformations among rectangular partitions |
| title_sort | transformations among rectangular partitions |
| topic | planar graph rectangular dual rectangularly dualizable graph rectangular partitions |
| url | https://toc.ui.ac.ir/article_26808_fbd1431a1ea5c85b2a6c397dacefc696.pdf |
| work_keys_str_mv | AT vinodkumar transformationsamongrectangularpartitions AT krishnendrashekhawat transformationsamongrectangularpartitions |