- Tytuł:
- A Note on Packing of Uniform Hypergraphs
- Autorzy:
-
Konarski, Jerzy
Woźniak, Mariusz
Żak, Andrzej - Powiązania:
- https://bibliotekanauki.pl/articles/32222532.pdf
- Data publikacji:
- 2022-11-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
packing
hypergraphs - Opis:
- We say that two n-vertex hypergraphs H1 and H2 pack if they can be found as edge-disjoint subhypergraphs of the complete hypergraph Kn. Whilst the problem of packing of graphs (i.e., 2-uniform hypergraphs) has been studied extensively since seventies, much less is known about packing of k-uniform hypergraphs for k ≥ 3. Naroski [Packing of nonuniform hypergraphs - product and sum of sizes conditions, Discuss. Math. Graph Theory 29 (2009) 651–656] defined the parameter mk(n) to be the smallest number m such that there exist two n-vertex k-uniform hypergraphs with total number of edges equal to m which do not pack, and conjectured that mk(n) = Θ (nk−1). In this note we show that this conjecture is far from being truth. Namely, we prove that the growth rate of mk(n) is of order nk/2 exactly for even k’s and asymptotically for odd k’s.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2022, 42, 4; 1383-1388
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki