Typical Structure of Oriented Graphs and Digraphs with Forbidden Blow-Up Transitive Triangles
Transitive tournament (including transitive triangle) and its blow-up have some symmetric properties. In this work, we establish an analogue result of the Erdös-Stone theorem of weighted digraphs with a forbidden blow-up of the transitive tournament. We give a stability result of oriented graphs and...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/12/2551 |
| _version_ | 1797406788268589056 |
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| author | Meili Liang Jianxi Liu |
| author_facet | Meili Liang Jianxi Liu |
| author_sort | Meili Liang |
| collection | DOAJ |
| description | Transitive tournament (including transitive triangle) and its blow-up have some symmetric properties. In this work, we establish an analogue result of the Erdös-Stone theorem of weighted digraphs with a forbidden blow-up of the transitive tournament. We give a stability result of oriented graphs and digraphs with forbidden blow-up transitive triangles and show that almost all oriented graphs and digraphs with forbidden blow-up transitive triangles are almost bipartite, which reconfirms and strengthens the conjecture of Cherlin. |
| first_indexed | 2024-03-09T03:31:41Z |
| format | Article |
| id | doaj.art-a456388b444f43a7a668725217849de1 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T03:31:41Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-a456388b444f43a7a668725217849de12023-12-03T14:55:17ZengMDPI AGSymmetry2073-89942022-12-011412255110.3390/sym14122551Typical Structure of Oriented Graphs and Digraphs with Forbidden Blow-Up Transitive TrianglesMeili Liang0Jianxi Liu1School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, ChinaSchool of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, ChinaTransitive tournament (including transitive triangle) and its blow-up have some symmetric properties. In this work, we establish an analogue result of the Erdös-Stone theorem of weighted digraphs with a forbidden blow-up of the transitive tournament. We give a stability result of oriented graphs and digraphs with forbidden blow-up transitive triangles and show that almost all oriented graphs and digraphs with forbidden blow-up transitive triangles are almost bipartite, which reconfirms and strengthens the conjecture of Cherlin.https://www.mdpi.com/2073-8994/14/12/2551forbidden digraphErdös-Stone theoremtransitive triangleblow-up |
| spellingShingle | Meili Liang Jianxi Liu Typical Structure of Oriented Graphs and Digraphs with Forbidden Blow-Up Transitive Triangles Symmetry forbidden digraph Erdös-Stone theorem transitive triangle blow-up |
| title | Typical Structure of Oriented Graphs and Digraphs with Forbidden Blow-Up Transitive Triangles |
| title_full | Typical Structure of Oriented Graphs and Digraphs with Forbidden Blow-Up Transitive Triangles |
| title_fullStr | Typical Structure of Oriented Graphs and Digraphs with Forbidden Blow-Up Transitive Triangles |
| title_full_unstemmed | Typical Structure of Oriented Graphs and Digraphs with Forbidden Blow-Up Transitive Triangles |
| title_short | Typical Structure of Oriented Graphs and Digraphs with Forbidden Blow-Up Transitive Triangles |
| title_sort | typical structure of oriented graphs and digraphs with forbidden blow up transitive triangles |
| topic | forbidden digraph Erdös-Stone theorem transitive triangle blow-up |
| url | https://www.mdpi.com/2073-8994/14/12/2551 |
| work_keys_str_mv | AT meililiang typicalstructureoforientedgraphsanddigraphswithforbiddenblowuptransitivetriangles AT jianxiliu typicalstructureoforientedgraphsanddigraphswithforbiddenblowuptransitivetriangles |