A perfect matching in a k-uniform hypergraph on n vertices, n divisible by k, is a set of n/k disjoint edges. In this paper we give a sufficient condition for the existence of a perfect matching in terms of a variant of the minimum degree. We prove that for every k ≥ 3 and sufficiently large n, a perfect matching exists in every n-vertex k-uniform hypergraph in which each set of k − 1 vertices ...

This letter shows that for every finite element triangulation in R, there exists a coloring where each triangle has exactly one red and two black edges. This result is shown using Petersen’s Theorem which states that all bridgeless 3-regular graphs have a perfect matching. The existence of such a coloring has useful applications when the finite element method is applied to problems with solutio...

For a family of connected graphs A , spanning subgraph H graph G is called an -factor if each component isomorphic to some in . has perfect 2-matching such that either edge or cycle, i.e. { P 2 C i | ≥ 3}-factor said be covered if, for every e ∈ E ( ), there M belongs deleted − possesses 2-matching. In this paper, we first obtain respective new characterizations bipartite and non-bipartite by p...

A decomposition of a graph is set subgraphs whose edges partition those $G$. The 3-decomposition conjecture posed by Hoffmann-Ostenhof in 2011 states that every connected cubic can be decomposed into spanning tree, 2-regular subgraph, and matching. It has been settled for special classes graphs, one the first results being Hamiltonian graphs. In past two years several new have obtained, adding ...

In this paper we deal with the following natural family of geometric matching problems. Given a class C of geometric objects and a point set P , a C-matching is a set M ⊆ C such that every C ∈ M contains exactly two elements of P . The matching is perfect if it covers every point, and strong if the objects do not intersect. We concentrate on matching points using axis-aligned squares and rectan...

This paper is on matching theory. A graph with perfect matching is called saturated if any addition of one complement edge creates a new perfect matching. Lovász gave a characterization of the saturated graphs called the cathedral theorem, and later Szigeti gave another proof. In this paper, we gave a new proof with our preceding works, which revealed the canonical structure of general graph wi...

A perfect matching in an undirected graph G = (V,E) is a set of vertex disjoint edges from E that include all vertices in V . The perfect matching problem is to decide if G has such a matching. Recently Rothvoß proved the striking result that the Edmonds’ matching polytope has exponential extension complexity. Here we describe a perfect matching polytope that is different from Edmonds’ polytope...

with rapid changes in the business environment, organizations are increasingly looking at human resources as a unique asset that can provide sustained competitive advantage. as much as, people are viewed among the most important resources to firms, hr strategy would be central to achieve competitive advantages .firms should view hr strategy as an important tool for integrating competencies insi...