منابع مشابه
On Hypergraphs of Girth Five
In this paper, we study r-uniform hypergraphs H without cycles of length less than five, employing the definition of a hypergraph cycle due to Berge. In particular, for r = 3, we show that if H has n vertices and a maximum number of edges, then |H| = 1 6 n + o(n). This also asymptotically determines the generalized Turán number T3(n, 8, 4). Some results are based on our bounds for the maximum s...
متن کاملOn Regular Hypergraphs of High Girth
We give lower bounds on the maximum possible girth of an r-uniform, d-regular hypergraph with at most n vertices, using the definition of a hypergraph cycle due to Berge. These differ from the trivial upper bound by an absolute constant factor (viz., by a factor of between 3/2 + o(1) and 2 + o(1)). We also define a random r-uniform ‘Cayley’ hypergraph on the symmetric group Sn which has girth Ω...
متن کاملGeneralized Girth Problems in Graphs and Hypergraphs
We study the asymptotic value of several extremal problems on graphs and hypergraphs, that arise as generalized notions of girth. Apart from being combinatorially natural questions, they are motivated by computational-theoretic applications. 1. An `-subgraph is a subgraph with ` edges per vertex, or equivalently, average degree 2`. What is the optimal upper bound S`(n, d), such that any graph o...
متن کاملBiregular Cages of Girth Five
Let 2 6 r < m and g be positive integers. An ({r,m}; g)–graph (or biregular graph) is a graph with degree set {r,m} and girth g, and an ({r,m}; g)–cage (or biregular cage) is an ({r,m}; g)–graph of minimum order n({r,m}; g). If m = r+1, an ({r,m}; g)–cage is said to be a semiregular cage. In this paper we generalize the reduction and graph amalgam operations from [M. Abreu, G. Araujo–Pardo, C. ...
متن کاملRamsey-type numbers involving graphs and hypergraphs with large girth
For a set of integers S, define ( S APk ) to be the k-uniform hypergraph with vertex set S and hyperedges corresponding to the set of all arithmetic progression of length k in S. Similarly, for a graph H, define ( H Kk ) to be the ( k 2 ) -uniform hypergraph on the vertex set E(H) with hyperedges corresponding to the edge sets of all copies of Kk in H. Also, we say that a k-uniform hypergraph h...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2003
ISSN: 1077-8926
DOI: 10.37236/1718