In this paper we use directed hypergraphs to represent the locality-based dependencies between the axioms of an OWL ontology. We define a notion of an axiom dependency hypergraph, where axioms are represented as nodes and dependencies between axioms as hyperedges connecting possibly several nodes with one node. We show that a locality-based module of an ontology corresponds to a connected compo...

Let k ≥ 2 be a fixed integer and P be a property of k-uniform hypergraphs. In other words, P is a (typically infinite) family of k-uniform hypergraphs and we say a given hypergraph H satisfies P if H ∈ P . For a given constant η > 0 a k-uniform hypergraph H on n vertices is η-far from P if no hypergraph obtained from H by changing (adding or deleting) at most ηn edges in H satisfies P . More pr...

A biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the associated edge-biclique hypergraph whose hyperedges are precisely the edge-sets of all bicliques. We characterize graphs whose edgebiclique hypergraph is conformal (i.e., it is the clique hypergraph of its 2-section) ...

A hypergraph pair is a pair (G,H) where G and H are hypergraphs on the same set of vertices. We extend the definitions of hypertree-width [7] and generalised hypertree-width [8] from hypergraphs to hypergraph pairs. We show that for constant k the problem of deciding whether a hypergraph pair has generalised hypertree-width ≤ k, is equivalent to the Hypergraph Sandwich Problem (HSP) [13]. It wa...

Let k be a positive integer and let G = (V,E) be a simple graph. The k-tuple domination number γ×k(G) of G is the minimum cardinality of a k-tuple dominating set S, a set that for every vertex v ∈ V , |NG[v]∩S| ≥ k. Also the total k-domination number γ×k,t(G) of G is the minimum cardinality of a total k -dominating set S, a set that for every vertex v ∈ V , |NG(v)∩S| ≥ k. The k-transversal numb...

The densest subgraph problem (DSG) aiming at finding an induced such that the average edge-weights of is maximized, a well-studied problem. However, when input graph hypergraph, existing notion DSG fails to capture fact hyperedge partially belonging sub-hypergraph also part sub-hypergraph. To resolve issue, we suggest function $$f_e:\mathbb {Z}_{\ge 0}\rightarrow \mathbb {R}_{\ge 0}$$ represent...

Generating minimal transversals of a hypergraph is an important problem which has many applications in Computer Science. In the present paper, we address this problem and its decisional variant, i.e., the recognition of the transversal hypergraph for another hypergraph. We survey some results on problems which are known to be related to computing the transversal hypergraph, where we focus on pr...

Coarse grain parallelism inherent in the solution of Linear Programming LP problems with block angular constraint matrices has been exploited in recent research works However these approaches su er from unscalability and load imbalance since they exploit only the exist ing block angular structure of the LP constraint matrix In this paper we consider decomposing LP constraint matrices to obtain ...

The competition hypergraph CH(D) of a digraph D is the hypergraph such that the vertex set is the same as D and e ⊆ V (D) is a hyperedge if and only if e contains at least 2 vertices and e coincides with the in-neighborhood of some vertex v in the digraph D. Any hypergraph H with sufficiently many isolated vertices is the competition hypergraph of an acyclic digraph. The hypercompetition number...

Let F be an r-uniform hypergraph and G be a multigraph. The hypergraph F is a Berge-G if there is a bijection f : E(G) → E(F) such that e ⊆ f(e) for each e ∈ E(G). Given a family of multigraphs G, a hypergraph H is said to be G-free if for each G ∈ G, H does not contain a subhypergraph that is isomorphic to a Berge-G. We prove bounds on the maximum number of edges in an r-uniform linear hypergr...