In this paper we study conditions which guarantee the existence of perfect matchings and perfect fractional matchings in uniform hypergraphs. We reduce this problem to an old conjecture by Erdős on estimating the maximum number of edges in a hypergraph when the (fractional) matching number is given, which we are able to solve in some special cases using probabilistic techniques. Based on these ...

Let ? be a finite, undirected, connected, simple graph. We say that matching M is permutable m -matching if contains edges and the subgroup of Aut ( ) fixes setwise allows to permuted in any fashion. A 2-transitive stabilizer can map ordered pair distinct other . provide constructions graphs with matching; we show that, an arc-transitive graph for ? 4 , then degree at least ; and, when sufficie...

For a certain graph obtained by adding extra vertices and edges to the triangular lattice graph, Propp conjectured that the number of perfect matchings of such a graph is always divisible by 3. In this note we prove this conjecture. In a graph G, a matching is a set of edges such that no two edges are incident to each other. A matching in a graph is called perfect if every vertex is incident wi...

Matching pada graf berarah merupakan himpunan bagian dari sisi tanpa simpul awal atau akhir yang sama. Simpul-simpul matching memiliki kaitan erat dengan multiplisitas geometri terbesar matriks ketetanggaan berarah. Penelitian ini bertujuan untuk mengidentifikasi maksimum Petersen pendekatan terbesar. Hasil penelitian menuntuujan bahwa 2 sikel faktor berkaitan graf, sedangkan mempunyai perfect ...

In 1993 Ruskey and Savage conjectured that in the d-dimensional hypercube, every matching M can be extended to a Hamiltonian cycle. Fink verified this for every perfect matching M , remarkably even if M contains external edges. We prove that this property also holds for sparse spanning regular subgraphs of the cubes: for every d ≥ 7 and every k, where 7 ≤ k ≤ d, the d-dimensional hypercube cont...