‎in this paper‎, ‎we give some necessary conditions for an $r$-partite graph such that the edge ring of the graph is cohen-macaulay‎. ‎it is proved that if there exists a cover of an $r$-partite cohen-macaulay graph by disjoint cliques of size $r$‎, ‎then such a cover is unique‎.

we find recursive formulae for the number of perfect matchings in a graph g by splitting g into subgraphs h and q. we use these formulas to count perfect matching of p hypercube qn. we also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in g, is the graph constructed from by deleting edges with an en...

We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...

‎In this paper‎, ‎we give some necessary conditions for an $r$-partite graph such that the edge ring of the graph is Cohen-Macaulay‎. ‎It is proved that if there exists a cover of an $r$-partite Cohen-Macaulay graph by disjoint cliques of size $r$‎, ‎then such a cover is unique‎.

Given an undirected network G(V,A,c) and a perfect matching M of G, the inverse maximum perfect matching problem consists of modifying minimally the elements of c so that M becomes a maximum perfect matching with respect to the modified vector. In this article, we consider the inverse problem when the modifications are measured by the weighted bottleneck-type Hamming distance. We propose an alg...

Given a set S of 2n points in R d , a perfect matching of S is a set of n edges such that each point of S is a vertex of exactly one edge. The weight of a perfect matching is the sum of the Euclidean lengths of all edges. Rao and Smith have recently shown that there is a constant r > 1, that only depends on the dimension d, such that a perfect matching whose weight is less than or equal to r ti...

For an arbitrary tree T, a T-matching in G is a set of vertex-disjoint subgraphs of G which are isomorphic to T. A T-matching which is a spanning subgraph of G is called a perfect T-matching. For any t-vertex tree T we find a threshold probability function jj = jj( n) for the existence of r edge-disjoint perfect T-matchings in a random graph G(n,p).

Extending the notion of (random) k-out graphs, we consider when the k-out hypergraph is likely to have a perfect fractional matching. In particular, we show that for each r there is a k = k(r) such that the k-out r-uniform hypergraph on n vertices has a perfect fractional matching with high probability (i.e., with probability tending to 1 as n → ∞) and prove an analogous result for r-uniform r-...

Let G = (V,E) be a weighted undirected graph with vertex set V , edge set E and a weight function d. Thus, d(u, v) denotes the weight of any edge (u, v) ∈ E. A matching M ⊆ E is a collection of edges such that every node in V is incident to at most one edge in M . The matching is perfect if every node in V is incident to exactly one edge in M . The cost of the matching is given by ∑ (u,v)∈M d(u...