On the maximum number of edges in a hypergraph with given matching number
نویسنده
چکیده
The aim of the present paper is to prove that the maximum number of edges in a 3-uniform hypergraph on n vertices and matching number s is max {(3s+ 2 3 ) , ( n 3 ) − ( n− s 3 )} for all n, s, n ≥ 3s+ 2.
منابع مشابه
ON THE MATCHING NUMBER OF AN UNCERTAIN GRAPH
Uncertain graphs are employed to describe graph models with indeterministicinformation that produced by human beings. This paper aims to study themaximum matching problem in uncertain graphs.The number of edges of a maximum matching in a graph is called matching numberof the graph. Due to the existence of uncertain edges, the matching number of an uncertain graph is essentially an uncertain var...
متن کاملOn the maximum number of edges in a hypergraph with a unique perfect matching
In this note, we determine the maximum number of edges of a k-uniform hypergraph, k ≥ 3, with a unique perfect matching. This settles a conjecture proposed by Snevily.
متن کاملOn the saturation number of graphs
Let $G=(V,E)$ be a simple connected graph. A matching $M$ in a graph $G$ is a collection of edges of $G$ such that no two edges from $M$ share a vertex. A matching $M$ is maximal if it cannot be extended to a larger matching in $G$. The cardinality of any smallest maximal matching in $G$ is the saturation number of $G$ and is denoted by $s(G)$. In this paper we study the saturation numbe...
متن کاملOn the Pixel Expansion of Hypergraph Access Structures in Visual Cryptography Schemes
In a visual cryptography scheme, a secret image is encoded into n shares, in the form of transparencies. The shares are then distributed to n participants. Qualified subsets of participants can recover the secret image by superimposing their transparencies, but non-qualified subsets of participants have no information about the secret image. Pixel expansion, which represents the number of subpi...
متن کاملOn the Maximum Number of Edges in a Triple System Not Containing a Disjoint Family of a Given Size
In 1965 Erdős conjectured a formula for the maximum number of edges in a kuniform n-vertex hypergraph without a matching of size s. We prove this conjecture for k = 3 and all s ≥ 1 and n ≥ 4s.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Applied Mathematics
دوره 216 شماره
صفحات -
تاریخ انتشار 2017