Let G be a graph that is a subgraph of some n-dimensional hypercube Qn. For sufficiently large n, Stout [20] proved that it is possible to pack vertexdisjoint copies of G in Qn so that any proportion r < 1 of the vertices of Qn are covered by the packing. We prove an analogous theorem for edge-disjoint packings: For sufficiently large n, it is possible to pack edge-disjoint copies of G in Qn so...

The bicontraction of a vertex v of degree two in a graph, with precisely two neighbours v1 and v2, consists of shrinking the set {v1, v, v2} to a single vertex. The retract of a matching covered graph G, denoted by Ĝ, is the graph obtained from G by repeatedly bicontracting vertices of degree two. Up to isomorphism, the retract of a matching covered graph G is unique. If G is a brace on six or ...

A set A of vertices in an r-uniform hypergraph H is covered in H if there is some vertex u 6∈ A such that every edge of form {u} ∪ B, B ∈ A(r−1) is in H. Erdős and Moser (1970) determined the minimum number of edges in a graph on n vertices such that every k-set is covered. We extend this result to r-uniform hypergraphs on sufficiently many vertices, and determine the extremal hypergraphs. We a...

Abstract A classification scheme for Graph-Like Modeling Languages (GLML) is presented in this paper. The novelty of classifier lies its application to a meta-model GLML that deviates from the simple graph model and underlies large number GLML. main goal using support reuse layout algorithms are used directly or indirectly development software by model-based engineering techniques. In other dom...

We characterize unmixed and Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs. also provide examples oriented graphs that have non-Cohen-Macaulay vertex-weighted ideals, while the ideal their underlying graph is Cohen-Macaulay. This disproves a conjecture posed by Pitones, Reyes, Toledo.

Barrier coverage is a critical issue in wireless sensor networks for many practical applications, e.g., national border monitoring, security surveillance and intruder detection, etc. Its aim is to detect intruders that attempt to cross the protected region. Available works mainly focused on the barrier coverage of directional sensors (e.g., cameras), which have limited coverage area and sensing...

For a fixed graph H; let f ðn;HÞ denote the maximum possible number of edges not belonging to a monochromatic copy of H in a 2-edge-coloring of the complete graph of order n: Let exðn;HÞ be the Turán number of H; i.e., the maximum number of edges that a graph on n vertices can have without containing a copy of H: An easy lower bound of f ðn;HÞXexðn;HÞ follows from the 2-edge-coloring in which t...

This paper presents a graph-based formalism for an Ontology Based Access Control (OBAC) system applied to Digital Library (DL) ontology. It uses graph transformations, a graphical specification technique based on a generalization of classical string grammars to nonlinear structures. The proposed formalism provides an executable specification that exploits existing tools of graph grammar to veri...

A set S ⊆ V (G) is stable (or independent) if no two vertices from S are adjacent. Let Ψ(G) be the family of all local maximum stable sets [6] of graph G, i.e., S ∈ Ψ(G) if S is a maximum stable set of the subgraph induced by S ∪ N(S), where N(S) is the neighborhood of S. If I is stable and there is a matching from N(I) into I, then I is a crown of order |I|+ |N(I)|, and we write I ∈ Crown(G) [...