K-uniform hypergraph
WebLet B i(k) be the k-uniform hypergraph whose vertex set is of the form S U T, where S = i, T = k - 1, and S∩T = φ, and whose edges are the k-subsets of S∪T that contain either S or T. We derive upper and lower bounds for the Turan density of B i (k) that are close to each other as k → ∞. Web1.4 (k,l)-Covering property We say a hypergraph H satisfies the (k,l)-covering property, or for short that H is a (k,l)-hypergraph, when any k edges of H can be covered using l vertices. The main problem of this thesis is to determine the maximum transversal number an r-uniform (k,l)-hypergraph can have, for a variety of regimes of r, k and l.
K-uniform hypergraph
Did you know?
WebFor 1 ‘ Webcase k≥ 4 and the case k= 2,3 was raised; this was considered evidence that the case k= 3 might be harder to understand. This difference has to do with the corresponding maximization problem called ‘Set-Splitting’, which is the problem of 2-coloring a k-uniform hypergraph while maximizing the number of non-monochromatic hyperedges. This ...
WebMar 16, 2009 · Hamilton l-cycles in uniform hypergraphs. Daniela Kühn, Richard Mycroft, Deryk Osthus. We say that a k-uniform hypergraph C is an l-cycle if there exists a cyclic ordering of the vertices of C such that every edge of C consists of k consecutive vertices and such that every pair of consecutive edges (in the natural ordering of the edges ...
WebAbstract. Let r ≥ k ≥ 2 and K r, n ( k) denote the complete n -balanced r -partite k -uniform hypergraph, whose vertex set consists of r parts, each has n vertices, and whose edge set … WebMay 1, 2012 · For a k-uniform hypergraph, one can obtain a straightforward generalization to an order-k array (essentially, a tensor), but in doing so, one loses the powerful and sophisticated tools of linear algebra with which to analyze it.
WebApr 11, 2024 · In 1999, Katona and Kierstead conjectured that if a -uniform hypergraph on vertices has minimum co-degree , i.e., each set of vertices is contained in at least edges, …
WebA k-graph H(also known as a k-uniform hypergraph), consists of a set of vertices V(H) and a set of edges E(H) fX V(H) : jXj= kg, so that each edge of Hconsists of k vertices. Let Hbe a k-graph, and let Abe a set of k 1 vertices of H. Then the degree of A, denoted d H(A), is the number of edges of Hwhich contain Aas a subset. The minimum gita press book storeWebAug 24, 2024 · Recently a variant of Ramsey numbers has been introduced for hypergraphs with a fixed order on their vertex sets [ 2, 5 ]. For an integer k \ge 2, an ordered k-uniform hypergraph \mathcal {H} is a pair (H,<) consisting of a k -uniform hypergraph H and a linear ordering < of its vertex set. funny js commandWebof a uniform hypergraph based on analysis of the largest eigenvalue of the adjacency tensor. As we know, the problem to find the clique number of a 2-uniform hypergraph(i.e. graph) is the NP-complete problem [8], and turns out to be even intractable to a k-uniform hypergraph for k ≥ 3. However, we have a good algorithm for calculating the ... funny josh allen fantasy football team namesWebIn a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present … gita press book onlineWebIn a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present paper continues the same line of study, … funny july 4th gifWebA k-graph H(also known as a k-uniform hypergraph), consists of a set of vertices V(H) and a set of edges E(H) fX V(H) : jXj= kg, so that each edge of Hconsists of k vertices. Let Hbe a … funny judge saying about coffeeWebk is the symmetric group on [k]. In the case of graphs, i.e., k= 2, cubical hypermatrices are simply square matrices, and symmetric hypermatrices are just symmetric matrices. funny july 4 shirts