Results 61 to 70 of about 622 (164)

Existential closure in uniform hypergraphs

Discrete Mathematics
For a positive integer $n$, a graph with at least $n$ vertices is $n$-existentially closed or simply $n$-e.c. if for any set of vertices $S$ of size $n$ and any set $T\subseteq S$, there is a vertex $x\not\in S$ adjacent to each vertex of $T$ and no vertex of $S\setminus T$.
Andrea C. Burgess, Robert D. Luther, David A. Pike   +2 more
openaire   +2 more sources

Partitioning 3-uniform hypergraphs

Journal of Combinatorial Theory, Series B, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ma, Jie, Yu, Xingxing
openaire   +1 more source

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
doaj   +1 more source

A Measure for the Vulnerability of Uniform Hypergraph Networks: Scattering Number

Mathematics
The scattering number of a graph G is defined as s(G)=max{ω(G−X)−|X|:X⊂V(G),ω(G−X)>1}, where X is a cut set of G, and ω(G−X) denotes the number of components in G−X, which can be used to measure the vulnerability of network G.
Ning Zhao, Haixing Zhao, Yinkui Li
doaj   +1 more source

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
doaj   +1 more source

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  

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

Cycle decompositions in k-uniform hypergraphs

Journal of Combinatorial Theory, Series B
v3: including referee comments.
Allan Lo, Simón Piga, Nicolás Sanhueza-Matamala   +2 more
openaire   +3 more sources

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

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