Results 91 to 100 of about 728,495 (209)
No‐(k+1)$(k+1)$‐in‐line problem for large constant k$k$
Bulletin of the London Mathematical Society, Volume 58, Issue 10, October 2026.Abstract How many points can be placed in an n×n$n\times n$ grid so that every (affine) line contains at most k$k$ points? We prove that for n⩾k⩾1037$n \geqslant k \geqslant 10^{37}$ the maximum number of points is exactly kn$kn$. Our proof builds on the recent work of Kovács, Nagy and Szabó (who proved an analogous result when k$k$ is at least about ...
Alexandr Grebennikov, Matthew Kwan
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Partial Total Domination in Hypergraphs
MathematicsThis paper establishes fundamental results for partial total domination in hypergraphs. We present tight bounds for the partial total domination number in k-uniform hypergraphs, demonstrate relationships with classical domination parameters, and provide ...
Abdulkafi Sanad, Chaoqian Li
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A note on a list colouring of hypergraphs [PDF]
Opuscula Mathematica, 2004 In the note we present two results. The first of them gives a sufficient condition for a colouring of a hypergraph from an assigned list. It generalises the analogous fact for graphs.
Ewa Drgas-Burchardt
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Almost Self-Complementary 3-Uniform Hypergraphs
Discussiones Mathematicae Graph Theory, 2017 It is known that self-complementary 3-uniform hypergraphs on n vertices exist if and only if n is congruent to 0, 1 or 2 modulo 4. In this paper we define an almost self-complementary 3-uniform hypergraph on n vertices and prove that it exists if and ...
Kamble Lata N. +2 more
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Super edge-magic labeling of m-node k-uniform hyperpaths and m-node k-uniform hypercycles
AKCE International Journal of Graphs and Combinatorics, 2016 We generalize the notion of the super edge-magic labeling of graphs to the notion of the super edge-magic labeling of hypergraphs. For a hypergraph H with a finite vertex set V and a hyperedge set E, a bijective function f:V∪E→{1,2,3,…,|V|+|E|} is called
Ratinan Boonklurb +2 more
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Bounded diameter monochromatic component covers
Mathematika, Volume 72, Issue 4, October 2026.Abstract Ryser conjectured that every r$r$‐edge‐coloured complete graph can be covered by r−1$r-1$ monochromatic trees. Motivated by a question of Austin in analysis, Milićević predicted something stronger — that every r$r$‐edge‐coloured complete graph can be covered by r−1$r-1$ monochromatic trees of bounded diameter.
Alexey Pokrovskiy
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3-uniform hypergraphs and linear cycles [PDF]
Electronic Notes in Discrete Mathematics, 2017 Improved the writing, more explanation added and corrections ...
Beka Ergemlidze +2 more
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Hypergraph Representation via Axis-Aligned Point-Subspace Cover [PDF]
Discrete Mathematics & Theoretical Computer ScienceWe propose a new representation of $k$-partite, $k$-uniform hypergraphs, that is, a hypergraph with a partition of vertices into $k$ parts such that each hyperedge contains exactly one vertex of each type; we call them $k$-hypergraphs for short.
Oksana Firman, Joachim Spoerhase
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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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