The α-Arboricity of Complete Uniform Hypergraphs

نویسندگان

  • Jean-Claude Bermond
  • Yeow Meng Chee
  • Nathann Cohen
  • Xiande Zhang
چکیده

α-acyclicity is an important notion in database theory. The α-arboricity of a hypergraphH is the minimum number of α-acyclic hypergraphs that partition the edge set of H. The α-arboricity of the complete 3-uniform hypergraph is determined completely.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Arboricity: An acyclic hypergraph decomposition problem motivated by database theory

The arboricity of a hypergraph H is the minimum number of acyclic hypergraphs that partition H . The determination of the arboricity of hypergraphs is a problem motivated by database theory. The exact arboricity of the complete k-uniform hypergraph of order n is previously known only for k ∈ {1, 2, n − 2, n − 1, n}. The arboricity of the complete k-uniform hypergraph of order n is determined as...

متن کامل

Directed domination in oriented hypergraphs

ErdH{o}s [On Sch"utte problem, Math. Gaz. 47 (1963)] proved that every tournament on $n$ vertices has a directed dominating set of at most $log (n+1)$ vertices, where $log$ is the logarithm to base $2$. He also showed that there is a tournament on $n$ vertices with no directed domination set of cardinality less than $log n - 2 log log n + 1$. This notion of directed domination number has been g...

متن کامل

Sparse Hypergraphs and Pebble Game Algorithms

A hypergraph G = (V, E) is (k, `)-sparse if no subset V ′ ⊂ V spans more than k|V ′|−` hyperedges. We characterize (k, `)-sparse hypergraphs in terms of graph theoretic, matroidal and algorithmic properties. We extend several well-known theorems of Haas, Lovász, Nash-Williams, Tutte, and White and Whiteley, linking arboricity of graphs to certain counts on the number of edges. We also address t...

متن کامل

Monochromatic Loose-cycle Partitions in Hypergraphs

In this paper we study the monochromatic loose-cycle partition problem for non-complete hypergraphs. Our main result is that in any r-coloring of a k-uniform hypergraph with independence number α there is a partition of the vertex set into monochromatic loose cycles such that their number depends only on r, k and α. We also give an extension of the following result of Pósa to hypergraphs: the v...

متن کامل

Note on Upper Density of Quasi-Random Hypergraphs

In 1964, Erdős proved that for any α > 0, an l-uniform hypergraph G with n > n0(α, l) vertices and α ( n l ) edges contains a large complete l-equipartite subgraph. This implies that any sufficiently large G with density α > 0 contains a large subgraph with density at least l!/ll. In this note we study a similar problem for l-uniform hypergraphs Q with a weak quasi-random property (i.e. with ed...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • SIAM J. Discrete Math.

دوره 25  شماره 

صفحات  -

تاریخ انتشار 2011