An H-decomposition of a graph G is a partition of the edge-set of G into subsets, where each subset induces a copy of the graph H. A k-orthogonal H-decomposition of a graph G is a set of k H-decompositions of G, such that any two copies of H in distinct H-decompositions intersect in at most one edge. In case G=Kn and H=Kr , a k-orthogonal Kr -decomposition of Kn is called an (n, r, k) completel...

We consider the class of graphs for which the edge connectivity is equal to the maximum number of edge-disjoint spanning trees, and the natural generalization to matroids, where the cogirth is equal to the number of disjoint bases. We provide descriptions of such graphs and matroids, showing that such a graph (or matroid) has a unique decomposition. In the case of graphs, our results are releva...

Given graphs G and H , an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H . Let φH(n) be the smallest number φ such that any graph G of order n admits an H-decomposition with at most φ parts. Here we study the case when H = C7, that is, the cycle of length 7 and prove that φC7(n) = n/4 for all n ≥ 10.

Given graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let φH(n) be the smallest number φ such that any graph G of order n admits an H-decomposition with at most φ parts. Here we determine the asymptotic of φH(n) for any fixed graph H as n tends to infinity. Partially supported by the Nation...

Geodetic numbers of graphs and digraphs have been investigated in the literature recently. The main purpose of this paper is to study the geodetic spectrum of a graph. For any two vertices u and v in an oriented graph D, a u–v geodesic is a shortest directed path from u to v. Let I (u, v) denote the set of all vertices lying on a u–v geodesic. For a vertex subset A, let I (A) denote the union o...

Let G be an undirected bipartite graph with positive integer weights on the edges. We refine the existing decomposition theorem originally proposed by Kao et al., for computing maximum weight bipartite matching. We apply it to design an efficient version of the decomposition algorithm to compute the weight of a maximum weight bipartite matching of G in O( √ |V |W ′/k(|V |,W ′/N))-time by employ...

For an ordered k-decomposition D = {G1, G2,...,Gk} of a connected graph G (V,E), the D-representation edge e is k-tuple γ(e/D)=(d(e, G1), d(e, G2), ...,d(e, Gk)), where Gi) represents distance from to Gi. A decomposition resolving if every two distinct edges have representations. The minimum k for which has its dimension dec(G). In this paper, corona product path Pn and cycle Cn with complete g...