Underlying Graphs of 3-Quasi-Transitive Digraphs and 3-Transitive Digraphs
A digraph is 3-quasi-transitive (resp. 3-transitive), if for any path x0x1 x2x3 of length 3, x0 and x3 are adjacent (resp. x0 dominates x3). C´esar Hern´andez-Cruz conjectured that if D is a 3-quasi-transitive digraph, then the underlying graph of D, UG(D), admits a 3-transitive orientation. In this...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2013-05-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.1680 |
| _version_ | 1827840339451314176 |
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| author | Wang Ruixia Wang Shiying |
| author_facet | Wang Ruixia Wang Shiying |
| author_sort | Wang Ruixia |
| collection | DOAJ |
| description | A digraph is 3-quasi-transitive (resp. 3-transitive), if for any path x0x1 x2x3 of length 3, x0 and x3 are adjacent (resp. x0 dominates x3). C´esar Hern´andez-Cruz conjectured that if D is a 3-quasi-transitive digraph, then the underlying graph of D, UG(D), admits a 3-transitive orientation. In this paper, we shall prove that the conjecture is true. |
| first_indexed | 2024-03-12T07:32:35Z |
| format | Article |
| id | doaj.art-7f2095b1fb284082bfa06d6530ced43d |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T07:32:35Z |
| publishDate | 2013-05-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-7f2095b1fb284082bfa06d6530ced43d2023-09-02T21:43:02ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922013-05-0133242943510.7151/dmgt.1680Underlying Graphs of 3-Quasi-Transitive Digraphs and 3-Transitive DigraphsWang Ruixia0Wang Shiying1School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi, 030006, PR ChinaSchool of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi, 030006, PR ChinaA digraph is 3-quasi-transitive (resp. 3-transitive), if for any path x0x1 x2x3 of length 3, x0 and x3 are adjacent (resp. x0 dominates x3). C´esar Hern´andez-Cruz conjectured that if D is a 3-quasi-transitive digraph, then the underlying graph of D, UG(D), admits a 3-transitive orientation. In this paper, we shall prove that the conjecture is true.https://doi.org/10.7151/dmgt.1680graph orientation3-quasi-transitive digraph3-transitive digraph |
| spellingShingle | Wang Ruixia Wang Shiying Underlying Graphs of 3-Quasi-Transitive Digraphs and 3-Transitive Digraphs Discussiones Mathematicae Graph Theory graph orientation 3-quasi-transitive digraph 3-transitive digraph |
| title | Underlying Graphs of 3-Quasi-Transitive Digraphs and 3-Transitive Digraphs |
| title_full | Underlying Graphs of 3-Quasi-Transitive Digraphs and 3-Transitive Digraphs |
| title_fullStr | Underlying Graphs of 3-Quasi-Transitive Digraphs and 3-Transitive Digraphs |
| title_full_unstemmed | Underlying Graphs of 3-Quasi-Transitive Digraphs and 3-Transitive Digraphs |
| title_short | Underlying Graphs of 3-Quasi-Transitive Digraphs and 3-Transitive Digraphs |
| title_sort | underlying graphs of 3 quasi transitive digraphs and 3 transitive digraphs |
| topic | graph orientation 3-quasi-transitive digraph 3-transitive digraph |
| url | https://doi.org/10.7151/dmgt.1680 |
| work_keys_str_mv | AT wangruixia underlyinggraphsof3quasitransitivedigraphsand3transitivedigraphs AT wangshiying underlyinggraphsof3quasitransitivedigraphsand3transitivedigraphs |