- Tytuł:
- Convex independence and the structure of clone-free multipartite tournaments
- Autorzy:
-
Parker, Darren
Westhoff, Randy
Wolf, Marty - Powiązania:
- https://bibliotekanauki.pl/articles/743115.pdf
- Data publikacji:
- 2009
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
convex sets
rank
Helly number
Radon number
multipartite tournaments - Opis:
- We investigate the convex invariants associated with two-path convexity in clone-free multipartite tournaments. Specifically, we explore the relationship between the Helly number, Radon number and rank of such digraphs. The main result is a structural theorem that describes the arc relationships among certain vertices associated with vertices of a given convexly independent set. We use this to prove that the Helly number, Radon number, and rank coincide in any clone-free bipartite tournament. We then study the relationship between Helly independence and Radon independence in clone-free multipartite tournaments. We show that if the rank is at least 4 or the Helly number is at least 3, then the Helly number and the Radon number are equal.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2009, 29, 1; 51-69
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł