Edmonds’ fundamental theorem on arborescences [4] characterizes the existence of k pairwise edge-disjoint arborescences with the same root in a directed graph. In [9], Lovász gave an elegant alternative proof which became the base of many extensions of Edmonds’ result. In this paper, we use a modification of Lovász’ method to prove a theorem on covering intersecting bi-set families under matroi...

a. To check that the graph is represented correctly, Bob asks Alice to remove all the paper cups covering the endpoints of every edge. This reveals an isomorphism to the original graph, which Bob cannot check efficiently; thus, Bob also removes the paper cups corresponding to the green numbers, revealing the original labelling of the vertices. This reveals nothing about the vertex cover, but al...

Absttact. A cactus graph is a connected graph in which every block is either an edge or a cycle. An optimal algorithm is presented here to find minimum cardinality 2-neighbourhood-covering set on cactus graphs in) (n O time, where n is the total number of vertices of the graph. The cactus graph has many applications in real life problems, specially in radio communication system.

We consider the problem of finding a transitive orientation of a comparability graph, such that the edge set of its covering graph contains a given subset of edges. We propose a solution which employs the classical technique of modular tree decomposition. The method leads to a polynomial time algorithm to construct such an orientation or report that it does not exist. © 2006 Elsevier B.V. All r...

The technique of counting cliques in networks is a natural problem. In this paper, we develop certain results on counting of triangles for the total graph of the Mycielski graph or central graph of star as well as completegraph families. Moreover, we discuss the upper bounds for the number of triangles in the Mycielski and other well known transformations of graphs. Finally, it is shown that th...

Let G = (V (G), E(G)) be a simple graph and H be a subgraph of G. G admits anH-covering, if every edge in E(G) belongs to at least one subgraph of G that is isomorphic to H. An (a, d)-H-antimagic total labeling of G is a bijection λ : V (G) ∪ E(G) → {1, 2, 3, . . . , |V (G)|+ |E(G)|} such that for all subgraphs H ′ isomorphic to H, the H ′ weights wt(H ) = ∑

A natural and practical criterion in the preparation of diagrams of ordered sets is to minimize the number of different slopes used for the edges. Any diagram requires at least the maximum number of upper covers (or of lower covers) of any element. While this maximum degree is not always enough we show that it is as long as any edge joining a covering pair may be bent, to produce a crooked diag...

A glued graph at K2-clone (K3-clone) results from combining two vertex-disjoint graphs by identifying an edge (a triangle) of each original graph. The clique covering numbers of these desired glued graphs have been investigated recently. Analogously, we obtain bounds of the clique partition numbers of glued graphs at K2-clones and K3-clones in terms of the clique partition numbers of their orig...