Results 121 to 130 of about 1,405,425 (255)

Small cores in 3-uniform hypergraphs

Journal of Combinatorial Theory, Series B, 2017
The main result of this paper is that for any $c>0$ and for large enough $n$ if the number of edges in a 3-uniform hypergraph is at least $cn^2$ then there is a core (subgraph with minimum degree at least 2) on at most 15 vertices. We conjecture that our result is not sharp and 15 can be replaced by 9.
David Solymosi, Jozsef Solymosi
openaire   +4 more sources

On the general sum-connectivity index of hypergraphs

AIMS Mathematics
Given a non-zero real number $ \alpha $, the general sum-connectivity index $ \chi_{\alpha} $ for graph $ G $ is given by the sum $ \Sigma_{xy\in {E(G)}} (d_x+d_y)^{\alpha} $. Here, $ d_x $ denotes the degree of a vertex $ x $ in graph $ G $, and $ E(G) $
Hongzhuan Wang, Piaoyang Yin, Yan Li
doaj   +1 more source

Hypergraphs with Pendant Paths are not Chromatically Unique

Discussiones Mathematicae Graph Theory, 2014
In this note it is shown that every hypergraph containing a pendant path of length at least 2 is not chromatically unique. The same conclusion holds for h-uniform r-quasi linear 3-cycle if r ≥ 2.
Tomescu Ioan
doaj   +1 more source

Hypergraph Representation via Axis-Aligned Point-Subspace Cover [PDF]

Discrete Mathematics & Theoretical Computer Science
We 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
doaj   +1 more source

Equitable Coloring ofk-Uniform Hypergraphs [PDF]

SIAM Journal on Discrete Mathematics, 2003
Let $H$ be a $k$-uniform hypergraph with $n$ vertices. A {\em strong $r$-coloring} is a partition of the vertices into $r$ parts, such that each edge of $H$ intersects each part. A strong $r$-coloring is called {\em equitable} if the size of each part is $\lceil n/r \rceil$ or $\lfloor n/r \rfloor$.
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Constructing and sampling partite, $3$-uniform hypergraphs with given degree sequence [PDF]

, 2023
Andras Hubai, Tamás Róbert Mezei, Ferenc Béres, András A. Benczúr, István Miklós   +4 more
openalex   +1 more source

Wickets in 3-uniform hypergraphs

Discrete Mathematics
In these notes, we consider a Turán-type problem in hypergraphs. What is the maximum number of edges if we forbid a subgraph? Let $H_n^{(3)}$ be a 3-uniform linear hypergraph, i.e. any two edges have at most one vertex common. A special hypergraph, called {\em wicket}, is formed by three rows and two columns of a $3 \times 3$ point matrix.
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On the Maximum Estrada Index of 3-Uniform Linear Hypertrees

The Scientific World Journal, 2014
For a simple hypergraph H on n vertices, its Estrada index is defined as EE(H)=∑i=1n‍eλi, where λ1,λ2,…,λn are the eigenvalues of its adjacency matrix. In this paper, we determine the unique 3-uniform linear hypertree with the maximum Estrada index.
Faxu Li, Liang Wei, Jinde Cao, Feng Hu, Haixing Zhao   +4 more
doaj   +1 more source

Characterization of the degree sequences of (quasi) regular uniform hypergraphs [PDF]

, 2013
Andrea Frosini, Christophe Picouleau, Simone Rinaldi   +2 more
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Equitable Orientations of Sparse Uniform Hypergraphs

The Electronic Journal of Combinatorics, 2016
Caro, West, and Yuster (2011) studied how $r$-uniform hypergraphs can be oriented in such a way that (generalizations of) indegree and outdegree are as close to each other as can be hoped. They conjectured an existence result of such orientations for sparse hypergraphs, of which we present a proof.
Cohen, Nathann, Lochet, William
openaire   +4 more sources