- Tytuł:
- The Second Neighbourhood for Bipartite Tournaments
- Autorzy:
-
Li, Ruijuan
Sheng, Bin - Powiązania:
- https://bibliotekanauki.pl/articles/31343394.pdf
- Data publikacji:
- 2019-05-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
second out-neighbourhood
out-neighbourhood
in-neighbourhood
bipartite tournament - Opis:
- Let T (X ∪ Y, A) be a bipartite tournament with partite sets X, Y and arc set A. For any vertex x ∈ X ∪Y, the second out-neighbourhood N++(x) of x is the set of all vertices with distance 2 from x. In this paper, we prove that T contains at least two vertices x such that |N++(x)| ≥ |N+(x)| unless T is in a special class ℬ1 of bipartite tournaments; show that T contains at least a vertex x such that |N++(x)| ≥ |N−(x)| and characterize the class ℬ2 of bipartite tournaments in which there exists exactly one vertex x with this property; and prove that if |X| = |Y | or |X| ≥ 4|Y |, then the bipartite tournament T contains a vertex x such that |N++(x)|+|N+(x)| ≥ 2|N−(x)|.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2019, 39, 2; 555-565
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki