Wyniki wyszukiwania

1

A Characterization of Hypergraphs with Large Domination Number

100%

Henning M. A., Löwenstein C.

Discussiones Mathematicae Graph Theory

|

2016

|

tom 36

|

nr 2

427-438

EN

Let H = (V, E) be a hypergraph with vertex set V and edge set E. A dominating set in H is a subset of vertices D ⊆ V such that for every vertex v ∈ V \ D there exists an edge e ∈ E for which v ∈ e and e ∩ D ≠ ∅. The domination number γ(H) is the minimum cardinality of a dominating set in H. It is known [Cs. Bujtás, M.A. Henning and Zs. Tuza, Transversals and domination in uniform hypergraphs, European J. Combin. 33 (2012) 62-71] that for k ≥ 5, if H is a hypergraph of order n and size m with all edges of size at least k and with no isolated vertex, then γ(H) ≤ (n + ⌊(k − 3)/2⌋m)/(⌊3(k − 1)/2⌋). In this paper, we apply a recent result of the authors on hypergraphs with large transversal number [M.A. Henning and C. Löwenstein, A characterization of hypergraphs that achieve equality in the Chvátal-McDiarmid Theorem, Discrete Math. 323 (2014) 69-75] to characterize the hypergraphs achieving equality in this bound.

2

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

The density Turan problem for 3-uniform linear hypertrees. An efficient testing algorithm

100%

Bielak H., Powroźnik K.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

|

2018

|

tom 72

|

nr 2

EN

Let \(\mathcal{T}=(V,\mathcal{E})\) be a 3-uniform linear hypertree. We consider a blow-up hypergraph \(\mathcal{B}[\mathcal{T}]\). We are interested in the following problem. We have to decide whether there exists a blow-up hypergraph \(\mathcal{B}[\mathcal{T}]\) of the hypertree \(\mathcal{T}\), with hyperedge densities satisfying some conditions, such that the hypertree \(\mathcal{T}\) does not appear in a blow-up hypergraph as a transversal. We present an efficient algorithm to decide whether a given set of hyperedge densities ensures the existence of a 3-uniform linear hypertree \(\mathcal{T}\) in a blow-up hypergraph \(\mathcal{B}[\mathcal{T}]\).

3

Generic saddle-node bifurcation for cascade second order ODEs on manifolds

88%

Medveď M.

Annales Polonici Mathematici

|

1998

|

tom 68

|

nr 3

211-225

EN

Cascade second order ODEs on manifolds are defined. These objects are locally represented by coupled second order ODEs such that any solution of one of them can represent an external force for the other one. A generic saddle-node bifurcation theorem for 1-parameter families of cascade second order ODEs is proved.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Discussiones Mathematicae Graph Theory

1 Bielak H.

1 Henning M. A.

1 Löwenstein C.

1 Medveď M.

1 Powroźnik K.

1 2018

1 2016

1 1998

A Characterization of Hypergraphs with Large Domination Number

The density Turan problem for 3-uniform linear hypertrees. An efficient testing algorithm

Generic saddle-node bifurcation for cascade second order ODEs on manifolds