Elementary lift and single element coextension of a binary gammoid
It is known that every binary elementary lift of a binary matroid is a matroid obtained by applying the splitting operation on that matroid. An elementary lift of a binary gammoid need not be a binary gammoid. This paper finds forbidden minors for the class of binary gammoids whose all elementary li...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-09-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2023.2278073 |
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| author | Shital Dilip Solanki Ganesh Mundhe S. B. Dhotre |
| author_facet | Shital Dilip Solanki Ganesh Mundhe S. B. Dhotre |
| author_sort | Shital Dilip Solanki |
| collection | DOAJ |
| description | It is known that every binary elementary lift of a binary matroid is a matroid obtained by applying the splitting operation on that matroid. An elementary lift of a binary gammoid need not be a binary gammoid. This paper finds forbidden minors for the class of binary gammoids whose all elementary lifts are binary gammoids by using the splitting operation. We also find forbidden minors for the class of binary gammoids whose every single element coextension is a binary gammoid. |
| format | Article |
| id | doaj-art-e599e99d019046ab877ceccb40fd84fc |
| institution | OA Journals |
| issn | 0972-8600 2543-3474 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj-art-e599e99d019046ab877ceccb40fd84fc2025-08-20T01:59:22ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742024-09-0121321922410.1080/09728600.2023.2278073Elementary lift and single element coextension of a binary gammoidShital Dilip Solanki0Ganesh Mundhe1S. B. Dhotre2Ajeenkya DY Patil University, Pune, Maharashtra, IndiaArmy Institute of Technology, Pune, Maharashtra, IndiaDepartment of Mathematics, Savitribai Phule Pune University, Pune, Maharashtra, IndiaIt is known that every binary elementary lift of a binary matroid is a matroid obtained by applying the splitting operation on that matroid. An elementary lift of a binary gammoid need not be a binary gammoid. This paper finds forbidden minors for the class of binary gammoids whose all elementary lifts are binary gammoids by using the splitting operation. We also find forbidden minors for the class of binary gammoids whose every single element coextension is a binary gammoid.https://www.tandfonline.com/doi/10.1080/09728600.2023.227807305B3505C8305C50Binary matroidsplittingbinary gammoid |
| spellingShingle | Shital Dilip Solanki Ganesh Mundhe S. B. Dhotre Elementary lift and single element coextension of a binary gammoid AKCE International Journal of Graphs and Combinatorics 05B35 05C83 05C50 Binary matroid splitting binary gammoid |
| title | Elementary lift and single element coextension of a binary gammoid |
| title_full | Elementary lift and single element coextension of a binary gammoid |
| title_fullStr | Elementary lift and single element coextension of a binary gammoid |
| title_full_unstemmed | Elementary lift and single element coextension of a binary gammoid |
| title_short | Elementary lift and single element coextension of a binary gammoid |
| title_sort | elementary lift and single element coextension of a binary gammoid |
| topic | 05B35 05C83 05C50 Binary matroid splitting binary gammoid |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2023.2278073 |
| work_keys_str_mv | AT shitaldilipsolanki elementaryliftandsingleelementcoextensionofabinarygammoid AT ganeshmundhe elementaryliftandsingleelementcoextensionofabinarygammoid AT sbdhotre elementaryliftandsingleelementcoextensionofabinarygammoid |