- Tytuł:
- Some remarks on the structure of strong $k$-transitive digraphs
- Autorzy:
-
Hernández-Cruz, César
Montellano-Ballesteros, Juan José - Powiązania:
- https://bibliotekanauki.pl/articles/30148710.pdf
- Data publikacji:
- 2014-11-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
digraph
transitive digraph
k-transitive digraph
quasi-transitive digraph
k-quasi-transitive digraph
Laborde-Payan-Xuong Conjecture - Opis:
- A digraph $D$ is $k$-transitive if the existence of a directed path ($v_0, v_1, . . ., v_k$), of length $k$ implies that ($v_0, v_k) ∈ A(D)$. Clearly, a 2-transitive digraph is a transitive digraph in the usual sense. Transitive digraphs have been characterized as compositions of complete digraphs on an acyclic transitive digraph. Also, strong 3 and 4-transitive digraphs have been characterized. In this work we analyze the structure of strong $k$-transitive digraphs having a cycle of length at least $k$. We show that in most cases, such digraphs are complete digraphs or cycle extensions. Also, the obtained results are used to prove some particular cases of the Laborde-Payan-Xuong Conjecture.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2014, 34, 4; 651-671
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł