Structure of edges in a 4-connected graph not contained in triangles and the number of contractible edges
Let be a 4-connected graph, and let denote the set of those edges of which are not contained in a triangle, and let denote the set of 4-contractible edges of . We show that if or , then unless has one of the three specified configurations.
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2018-08-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1016/j.akcej.2017.09.002 |
| _version_ | 1818259785295855616 |
|---|---|
| author | Yoshimi Egawa Keiko Kotani Shunsuke Nakamura |
| author_facet | Yoshimi Egawa Keiko Kotani Shunsuke Nakamura |
| author_sort | Yoshimi Egawa |
| collection | DOAJ |
| description | Let be a 4-connected graph, and let denote the set of those edges of which are not contained in a triangle, and let denote the set of 4-contractible edges of . We show that if or , then unless has one of the three specified configurations. |
| first_indexed | 2024-12-12T18:20:57Z |
| format | Article |
| id | doaj.art-8faa92566e6b438f973e9eb11b5187f0 |
| institution | Directory Open Access Journal |
| issn | 0972-8600 |
| language | English |
| last_indexed | 2024-12-12T18:20:57Z |
| publishDate | 2018-08-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-8faa92566e6b438f973e9eb11b5187f02022-12-22T00:16:09ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002018-08-0115220221010.1016/j.akcej.2017.09.00212092657Structure of edges in a 4-connected graph not contained in triangles and the number of contractible edgesYoshimi Egawa0Keiko Kotani1Shunsuke Nakamura2Department of Applied Mathematics, Tokyo University of Science Shinjuku-kuDepartment of Mathematics, Tokyo University of Science Shinjuku-kuDepartment of Applied Mathematics, Tokyo University of Science Shinjuku-kuLet be a 4-connected graph, and let denote the set of those edges of which are not contained in a triangle, and let denote the set of 4-contractible edges of . We show that if or , then unless has one of the three specified configurations.http://dx.doi.org/10.1016/j.akcej.2017.09.0024-connected graphcontractible edgetriangle |
| spellingShingle | Yoshimi Egawa Keiko Kotani Shunsuke Nakamura Structure of edges in a 4-connected graph not contained in triangles and the number of contractible edges AKCE International Journal of Graphs and Combinatorics 4-connected graph contractible edge triangle |
| title | Structure of edges in a 4-connected graph not contained in triangles and the number of contractible edges |
| title_full | Structure of edges in a 4-connected graph not contained in triangles and the number of contractible edges |
| title_fullStr | Structure of edges in a 4-connected graph not contained in triangles and the number of contractible edges |
| title_full_unstemmed | Structure of edges in a 4-connected graph not contained in triangles and the number of contractible edges |
| title_short | Structure of edges in a 4-connected graph not contained in triangles and the number of contractible edges |
| title_sort | structure of edges in a 4 connected graph not contained in triangles and the number of contractible edges |
| topic | 4-connected graph contractible edge triangle |
| url | http://dx.doi.org/10.1016/j.akcej.2017.09.002 |
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