- Tytuł:
- Asymptotic Sharpness of Bounds on Hypertrees
- Autorzy:
-
Lin, Yi
Kang, Liying
Shan, Erfang - Powiązania:
- https://bibliotekanauki.pl/articles/31341637.pdf
- Data publikacji:
- 2017-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
hypertree
semicycle in hypergraph
chain in hypergraph - Opis:
- The hypertree can be defined in many different ways. Katona and Szabó introduced a new, natural definition of hypertrees in uniform hypergraphs and investigated bounds on the number of edges of the hypertrees. They showed that a $k$-uniform hypertree on $n$ vertices has at most \( \binom{n}{k−1} \) edges and they conjectured that the upper bound is asymptotically sharp. Recently, Szabó verified that the conjecture holds by recursively constructing an infinite sequence of $k$-uniform hypertrees and making complicated analyses for it. In this note we give a short proof of the conjecture by directly constructing a sequence of $k$-uniform $k$-hypertrees.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2017, 37, 3; 789-795
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł