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...

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...

K-way hypergraph partitioning has an ever-growing use in parallelization of scientific computing applications. We claim that hypergraph partitioning with multiple constraints and fixed vertices should be implemented using direct K-way refinement, instead of the widely adopted recursive bisection paradigm. Our arguments are based on the fact that recursive-bisection-based partitioning algorithms...

Alon, Kleitman, Lipton, Meshulam, Rabin and Spencer (Graphs. Combin. 7 (1991), no. 2, 97-99) proved, that for any hypergraph F = fF1; F2; : : : ; Fd(q 1)+1g, where q is a primepower, and d denotes the maximal degree of the hypergraph, there exists an F0 F , such that jSF2F0 F j 0 (mod q). We give a direct, alternative proof for this theorem, and we also give an explicit construction of a hyperg...

In this paper we consider the problem of determining all values of v for which there exists a decomposition of the complete 3-uniform hypergraph on v vertices into edge-disjoint copies of a given 3-uniform hypergraph. We solve the problem for each 3-uniform hypergraph having at most three edges and at most six vertices, and for the 3-uniform hypergraph of order 6 whose edges form the lines of t...

The paper considers the problem of computing a maximal independent set in a hypergraph (see 3] and 7]). We present an eecient deterministic NC algorithm for nding a maximal independent set in a hypergraph of dimension 3: the algorithm runs in time O(log 4 n) time on n + m processors of an EREW PRAM and is optimal up to a polylogarithmic factor. Our algorithm adapts the technique of Goldberg and...