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Spatial transcriptomic profiling reveals distinct signatures in acute versus chronic wounds through hypergraph modelling and transcriptomic entropy analysis

Sharps MC, Herrera JA, Moscalu R, Wright LI, Garner T, Murtuza Baker S, Reid A, Stevens A, Wong J.   +8 more
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Non-uniform hypergraphs

2020
Summary: Non-uniform hypergraphs are a generalization of hypergraphs in which not all edges need to have the same cardinality. It allows them to support a more complex data structure. In this paper, we extend some results for non-uniform hypergraphs and generalize the spectral results for uniform hypergraphs to non-uniform hypergraphs.
Shirdel, Gholam Hassan, Mortezaee, Ameneh, Golpar-raboky, Effat   +2 more
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The Uniformity Lemma for hypergraphs

Graphs and Combinatorics, 1992
This is an extension of Szemerédi's theorem called the Uniformity Lemma for Graphs (see \textit{E. Szemerédi} [Problèmes combinatoires et théorie des graphes, Orsay 1976, Colloq. int. CNRS No. 260, 399-401 (1978; Zbl 0413.05055)]) to \(r\)-uniform hypergraphs. Two applications of the result are announced: proof of a conjecture of Erdős concerning Turán-
Frankl, Peter, Rödl, Vojtěch
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Relative Turán Problems for Uniform Hypergraphs

SIAM Journal on Discrete Mathematics, 2021
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Spiro, Sam, Verstraëte, Jacques
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2-Colorings of uniform hypergraphs

Mathematical Notes, 2016
One of the most popular and classical extremal problems in hypergraph theory is the property of the existence \(2\)-coloring of its vertex set such that no hyper-edge of the hypergraph concerned is monochromatic. Certain bounds for the least number \(m(n)\) of edges of an \(n\)-uniform hypergraph with this property have been determined in the recent ...
Demidovich, Yu. A., Raigorodskii, A. M.
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Self-Complementary Non-Uniform Hypergraphs

Graphs and Combinatorics, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Intersection Multigraphs of Uniform Hypergraphs

Graphs and Combinatorics, 1998
A hypergraph \(H=(V,\{X_i \mid i\in I\})\) is \(k\)-uniform if all hyperedges \(X_i\) have the same cardinality \(k\); it is \(k\)-conformal if there is some graph \(G\) such that \(H\) is isomorphic to the hypergraph of all cliques with \(k\) vertices of \(G\).
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Partitioning dense uniform hypergraphs

Journal of Combinatorial Optimization, 2017
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Wu, Shufei, Hou, Jianfeng
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Regularity Lemma for k‐uniform hypergraphs

Random Structures & Algorithms, 2004
AbstractSzemerédi's Regularity Lemma proved to be a very powerful tool in extremal graph theory with a large number of applications. Chung [Regularity lemmas for hypergraphs and quasi‐randomness, Random Structures Algorithms 2 (1991), 241–252], Frankl and Rödl [The uniformity lemma for hypergraphs, Graphs Combin 8 (1992), 309–312; Extremal problems on ...
Rödl, Vojtěch, Skokan, Jozef
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