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About a generalization of transversals

Martin Kochol (1994)

Mathematica Bohemica

The aim of this paper is to generalize several basic results from transversal theory, primarily the theorem of Edmonds and Fulkerson.

On the total k-domination number of graphs

Adel P. Kazemi (2012)

Discussiones Mathematicae Graph Theory

Let k be a positive integer and let G = (V,E) be a simple graph. The k-tuple domination number γ × k ( G ) of G is the minimum cardinality of a k-tuple dominating set S, a set that for every vertex v ∈ V, | N G [ v ] S | k . Also the total k-domination number γ × k , t ( G ) of G is the minimum cardinality of a total k -dominating set S, a set that for every vertex v ∈ V, | N G ( v ) S | k . The k-transversal number τₖ(H) of a hypergraph H is the minimum size of a subset S ⊆ V(H) such that |S ∩e | ≥ k for every edge e ∈ E(H). We know that for any graph...

Quasigroups arisen by right nuclear extension

Péter T. Nagy, Izabella Stuhl (2012)

Commentationes Mathematicae Universitatis Carolinae

The aim of this paper is to prove that a quasigroup Q with right unit is isomorphic to an f -extension of a right nuclear normal subgroup G by the factor quasigroup Q / G if and only if there exists a normalized left transversal Σ Q to G in Q such that the right translations by elements of Σ commute with all right translations by elements of the subgroup G . Moreover, a loop Q is isomorphic to an f -extension of a right nuclear normal subgroup G by a loop if and only if G is middle-nuclear, and there exists...

Symmetrized and continuous generalization of transversals

Martin Kochol (1996)

Mathematica Bohemica

The theorem of Edmonds and Fulkerson states that the partial transversals of a finite family of sets form a matroid. The aim of this paper is to present a symmetrized and continuous generalization of this theorem.

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