Results 11 to 20 of about 8,142 (223)
Discussiones Mathematicae Graph Theory, 2016 If D = (V,A) is a digraph, its niche hypergraph NH(D) = (V, E) has the edge set ℇ = {e ⊆ V | |e| ≥ 2 ∧ ∃ v ∈ V : e = N−D(v) ∨ e = N+D(v)}. Niche hypergraphs generalize the well-known niche graphs (see [11]) and are closely related to competition ...
Garske Christian +2 more
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Lagrangians of Hypergraphs [PDF]
Combinatorics, Probability and Computing, 2002 How large can the Lagrangian of an r-graph with m edges be? Frankl and Füredi [1] conjectured that the r-graph of size m formed by taking the first m sets in the colex ordering of N(r) has the largest Lagrangian of all r-graphs of size m. We prove the first ‘interesting’ case of this conjecture, namely that the 3-graph with (t3) edges and ...
Talbot, JM
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Resolvability in Hypergraphs [PDF]
Contributions to Discrete Mathematics, 2023 This article presents an extension of the study of metric and partition dimension to hypergraphs. We give sharp lower bounds for the metric and partition dimension of hypergraphs in general and give exact values under specified conditions.
Imran Javaid +3 more
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Decomposing hypergraphs into k-colorable hypergraphs [PDF]
Transactions on Combinatorics, 2014 For a given hypergraph $H$ with chromatic number $chi(H)$ and with no edge containing only one vertex, it is shown that the minimum number $l$ for which there exists a partition (also a covering) ${E_1,E_2,ldots,E_l}$ for $E(H)$, such that the ...
Gholamreza Omidi , Khosro Tajbakhsh
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Hypergraph convolution and hypergraph attention [PDF]
Pattern Recognition, 2021 Recently, graph neural networks have attracted great attention and achieved prominent performance in various research fields. Most of those algorithms have assumed pairwise relationships of objects of interest. However, in many real applications, the relationships between objects are in higher-order, beyond a pairwise formulation.
Song Bai 0001 +2 more
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Hypergraph Based Berge Hypergraphs [PDF]
Graphs and Combinatorics, 2021 Fix a hypergraph $\mathcal{F}$. A hypergraph $\mathcal{H}$ is called a {\it Berge copy of $\mathcal{F}$} or {\it Berge-$\mathcal{F}$} if we can choose a subset of each hyperedge of $\mathcal{H}$ to obtain a copy of $\mathcal{F}$. A hypergraph $\mathcal{H}$ is {\it Berge-$\mathcal{F}$-free} if it does not contain a subhypergraph which is Berge copy of $\
Martin Balko +4 more
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Journal of Combinatorial Theory, Series B, 2021 The following very natural problem was raised by Chung and Erdős in the early 80's and has since been repeated a number of times. What is the minimum of the Turán number $\text{ex}(n,\mathcal{H})$ among all $r$-graphs $\mathcal{H}$ with a fixed number of edges?
Matija Bucic +3 more
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, 2022 Here we prove the following result from finite set theory. Given a family S of five subsets of a 10-set, suppose |A△B|≥6 for all distinct A,B∈S. Prove that |A△B|=6 for all distinct A,B∈S.
Elmar Guseinov (13785133)
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Quasirandomness in hypergraphs [PDF]
Electronic Notes in Discrete Mathematics, 2017 An $n$-vertex graph $G$ of edge density $p$ is considered to be quasirandom if it shares several important properties with the random graph $G(n,p)$. A well-known theorem of Chung, Graham and Wilson states that many such `typical' properties are asymptotically equivalent and, thus, a graph $G$ possessing one such property automatically satisfies the ...
Elad Aigner-Horev +4 more
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, 2011 A support of a hypergraph H is a graph with the same vertex set as H in which each hyperedge induces a connected subgraph. We show how to test in polynomial time whether a given hypergraph has a cactus support, i.e. a support that is a tree of edges and cycles.
Brandes, Ulrik +3 more
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