Integer and fractional packings in dense 3-uniform hypergraphs
نویسندگان
چکیده
منابع مشابه
Integer and fractional packings in dense 3-uniform hypergraphs
Let 0 be any fixed 3-uniform hypergraph. For a 3-uniform hypergraph we define 0( ) to be the maximum size of a set of pairwise triple-disjoint copies of 0 in . We say a function from the set of copies of 0 in to [0, 1] is a fractional 0-packing of if ¥ e ( ) 1 for every triple e of . Then * 0( ) is defined to be the maximum value of ¥ 0 over all fractional 0-packings of . We show that * 0( ) 0(...
متن کاملInteger and fractional packings of hypergraphs
Let F0 be a fixed k-uniform hypergraph. The problem of finding the integer F0-packing number νF0 (H) of a k-uniform hypergraph H is an NP-hard problem. Finding the fractional F0-packing number ν∗ F0 (H) however can be done in polynomial time. In this paper we give a lower bound for the integer F0-packing number νF0 (H) in terms of ν∗ F0 (H) and show that νF0 (H) ≥ ν∗ F0 (H)− o(|V (H)| k).
متن کاملInteger and Fractional Packings in Dense Graphs
Let H 0 be any xed graph. For a graph G we deene H 0 (G) to be the maximum size of a set of pairwise edge-disjoint copies of H 0 in G. We say a function from the set of copies of H 0 in G to 0; 1] is a fractional H 0-packing of G if
متن کاملFractional and integer matchings in uniform hypergraphs
A conjecture of Erdős from 1965 suggests the minimum number of edges in a kuniform hypergraph on n vertices which forces a matching of size t, where t ≤ n/k. Our main result verifies this conjecture asymptotically, for all t < 0.48n/k. This gives an approximate answer to a question of Huang, Loh and Sudakov, who proved the conjecture for t ≤ n/3k. As a consequence of our result, we extend bound...
متن کاملInteger and fractional packings in dense graphs: A simpler proof
Let H0 be a fixed connected graph. For a graph G, the H0-packing number, denoted νH0(G), is the maximum number of pairwise edge-disjoint copies of H0 in G. A function ψ from the set of copies of H0 in G to [0, 1] is a fractional H0-packing of G if ∑ e∈H ψ(H) ≤ 1 for each e ∈ E(G). The fractional H0-packing number, denoted ν H0(G), is defined to be the maximum value of ∑ H∈( G H0) ψ(H) over all ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2003
ISSN: 1042-9832
DOI: 10.1002/rsa.10075