Results 101 to 110 of about 730,755 (216)
Simonovits's theorem in random graphs
Proceedings of the London Mathematical Society, Volume 133, Issue 4, October 2026.Abstract Let H$H$ be a graph with χ(H)=r+1$\chi (H) = r+1$. Simonovits's theorem states that, if H$H$ is edge‐critical, the unique largest H$H$‐free subgraph of Kn$K_n$ is its largest r$r$‐partite subgraph, provided that n$n$ is sufficiently large. We show that the same holds with Kn$K_n$ replaced by the binomial random graph Gn,p$G_{n,p}$ whenever H$H$
Ilay Hoshen, Wojciech Samotij
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Judicious partitions of uniform hypergraphs [PDF]
Combinatorica, 2014 The vertices of any graph with $m$ edges may be partitioned into two parts so that each part meets at least $\frac{2m}{3}$ edges. Bollobás and Thomason conjectured that the vertices of any $r$-uniform hypergraph with $m$ edges may likewise be partitioned into $r$ classes such that each part meets at least $\frac{r}{2r-1}m$ edges. In this paper we prove
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Engineering Reports, Volume 8, Issue 9, September 2026.Selecting build‐to‐suit telecom contractors is a high‐stakes decision shaped by vague expert judgments. This study develops an interval type‐3 fuzzy Analytic Hierarchy Process whose secondary credibility grade models uncertainty about the judgments themselves.
Leah‐Maria Ndokezi, Haryson Nyobuya
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Engineering Reports, Volume 8, Issue 9, September 2026.The HGN‐MSP model addresses academic performance prediction challenges through multimodal graph learning with semantic alignment and modality balancing, achieving 0.896 AUC and 5.3% improvement over XGBoost in precisely identifying at‐risk students on a dataset of 19,856 students.
Jun Fan, Bin Chen, Byungwon Min, Tao Xie
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Hamiltonicity and $\sigma$-hypergraphs
Theory and Applications of Graphs, 2014 We define and study a special type of hypergraph. A $\sigma$-hypergraph $H= H(n,r,q$ $\mid$ $\sigma$), where $\sigma$ is a partition of $r$, is an $r$-uniform hypergraph having $nq$ vertices partitioned into $ n$ classes of $q$ vertices each.
Christina Zarb
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On Tight Tree‐Complete Hypergraph Ramsey Numbers
Journal of Graph Theory, Volume 113, Issue 1, Page 88-96, September 2026.ABSTRACT Chvátal showed that for any tree T with k edges, the Ramsey number R ( T , n ) = k ( n − 1 ) + 1. For r = 3 or 4, we show that, if T is an r‐uniform nontrivial tight tree, then the hypergraph Ramsey number R ( T , n ) = Θ ( n r − 1 ). The 3‐uniform result comes from observing a construction of Cooper and Mubayi.
Jiaxi Nie
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Reducing hypergraph coloring to clique search [PDF]
, 2019 It is known that the legal coloring of the nodes of a given graph can be reduced to a clique search problem. This paper generalizes this result for hypergraphs. Namely, we will show how legal coloring of the nodes of a hypergraph can be reduced to clique
Szabó, Sándor, Zavalnij, Bogdan
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Transversal numbers of uniform hypergraphs
Graphs and Combinatorics, 1990 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A note on self-complementary 4-uniform hypergraphs [PDF]
Opuscula Mathematica, 2005 We prove that a permutation \(\theta\) is complementing permutation for a \(4\)-uniform hypergraph if and only if one of the following cases is satisfied: (i) the length of every cycle of \(\theta\) is a multiple of \(8\), (ii) \(\theta\) has \(1\), \(2\)
Artur Szymański
doaj
Constrained Colouring and σ-Hypergraphs
Discussiones Mathematicae Graph Theory, 2015 A constrained colouring or, more specifically, an (α, β)-colouring of a hypergraph H, is an assignment of colours to its vertices such that no edge of H contains less than α or more than β vertices with different colours.
Caro Yair, Lauri Josef, Zarb Christina
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