Results 81 to 90 of about 7,886 (170)
Regular subgraphs of uniform hypergraphs
Journal of Combinatorial Theory, Series B, 2016 We prove that for every integer $r\geq 2$, an $n$-vertex $k$-uniform hypergraph $H$ containing no $r$-regular subgraphs has at most $(1+o(1)){{n-1}\choose{k-1}}$ edges if $k\geq r+1$ and $n$ is sufficiently large. Moreover, if $r\in\{3,4\}$, $r\mid k$ and $k,n$ are both sufficiently large, then the maximum number of edges in an $n$-vertex $k$-uniform ...
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A Tight Bound for Hyperaph Regularity
Geometric and Functional Analysis, 2019 This manuscript contains the proof of the main result of arXiv:1907.07639 when specialized to 3-uniform ...
Moshkovitz, Guy, Shapira, Asaf
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Nearly Hamilton cycles in sublinear expanders and applications
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract We develop novel methods for constructing nearly Hamilton cycles in sublinear expanders with good regularity properties, as well as new techniques for finding such expanders in general graphs. These methods are of independent interest due to their potential for various applications to embedding problems in sparse graphs.
Shoham Letzter +2 more
wiley +1 more source
Randomized Hypergraph States and Their Entanglement Properties
Annalen der Physik, Volume 538, Issue 1, January 2026.Randomized hypergraph (RH) states are mixed states that extend the concept of randomized graph states to multi‐qubit hypergraphs subject to probabilistic gate imperfections. By modeling noisy multi‐qubit operations, this work reveals nonmonotonic behavior in bipartite and multipartite entanglement, derives analytical witnesses for specific hypergraph ...
Vinícius Salem +2 more
wiley +1 more source
Indecomposable regular graphs and hypergraphs
Discrete Mathematics, 1992 A hypergraph \(H\) consists of a finite nonempty set \(V(H)\) called the vertex set and a collection \(E(H)\) (called the edge set of \(H)\) of subsets of the power set of \(V(H)\). Note \(E(H)\) may contain the same set more then once. The number of times an element \(e\) in \(E(H)\) appears in \(E(H)\) is called its multiplicity denoted by \(m_ H(e)\)
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Hypergraphs, Quasi-randomness, and Conditions for Regularity
Journal of Combinatorial Theory, Series A, 2002 The study of quasi-randomness is a flourishing topic on uniform hypergraphs. F. R. K. Chung and R. L. Graham (among others) investigated thoroughly quasi-random uniform hypergraphs of density 1/2, showing a series of important equivalent statements about these structures. In this investigations the notion of deviation plays a central role.
Kohayakawa, Yoshiharu +2 more
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A note on the random greedy independent set algorithm
, 2015 Let r be a fixed constant and let H be an r-uniform, D-regular hypergraph on N vertices. Assume further that D > N^\epsilon for some \epsilon>0. Consider the random greedy algorithm for forming an independent set in H.
Bennett, Patrick, Bohman, Tom
core
Eigenvalues of non-regular linear quasirandom hypergraphs
Discrete Mathematics, 2017 15 pages. (this paper was originally part of an old version of arXiv:1208.4863)
Lenz, John, Mubayi, Dhruv
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A Simple Regularization of Hypergraphs
, 2006 We give a simple and natural (probabilistic) construction of hypergraph regularization. It is done just by taking a constant-bounded number of random vertex samplings only one time (thus, iteration-free). It is independent from the definition of quasi-randomness and yields a new elementary proof of a strong hypergraph regularity lemma. Consequently, as
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Regular embedding of simple hypergraphs
Regular hypermaps with underlying simple hypergraphs are analysed. We obtain an algorithm to classify the regular embeddings of simple hypergraphs with given order, and determine the automorphism groups of regular embedding of simple hypergraphs with prime square order.
Zhu, Yanhong, Yuan, Kai
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