Given a set of propositions, one can consider its inconsistency hypergraph. Then the safisfiability of sets of clauses with respect to that hypergraph (see [2], [4]) turns out to be the usual satisfiability. The problem is which hypergraphs can be obtained from sets of formulas as inconsistency hypergraphs. In the present paper it is shown that this can be done for all hypergraphs with countabl...

Fundamental local symmetry breaking problems such as Maximal Independent Set (MIS) and coloring have been recognized as important by the community, and studied extensively in (standard) graphs. In particular, fast (i.e., logarithmic run time) randomized algorithms are well-established for MIS and ∆ + 1-coloring in both the LOCAL and CONGEST distributed computing models. On the other hand, compa...

Recently, Storm [10] defined the Ihara-Selberg zeta function of a hypergraph, and gave two determinant expressions of it by the Perron-Frobenius operator of a digraph and a deformation of the usual Laplacian of a graph. We present a new determinant expression for the Ihara-Selberg zeta function of a hypergraph, and give a linear algebraic proof of Storm’s Theorem. Furthermore, we generalize the...

We prove that the vertex degree threshold for tiling C3 4 (the 3-uniform hypergraph with four vertices and two triples) in a 3-uniform hypergraph on n ∈ 4N vertices is (n−1 2 ) − ( 4 n 2 ) + 8n + c, where c = 1 if n ∈ 8N and c = −2 otherwise. This result is best possible, and is one of the first results on vertex degree conditions for hypergraph tiling. C © 2014 Wiley Periodicals, Inc. J. Graph...

Recently, Storm [8] defined the Ihara-Selberg zeta function of a hypergraph, and gave two determinant expressions of it. We define the Bartholdi zeta function of a hypergraph, and present a determinant expression of it. Furthermore, we give a determinant expression for the Bartholdi zeta function of semiregular bipartite graph. As a corollary, we obtain a decomposition formula for the Bartholdi...

Community extraction plays an important role in network analysis. This paper discusses communities in hypergraphs. Since hypergraphs can represent multi-relational networks, they are important structures in many domains. In this study, the definition of communities based on the number of adjacent links/nodes is extended to a hypergraph. Four extended models are proposed. The adequacy of these m...

A hypergraph or “packed forest” is a compact data structure that uses structure-sharing to represent exponentially many trees in polynomial space. A probabilistic/weighted hypergraph also defines a probability (or other weight) for each tree, and can be used to represent the hypothesis space considered (for a given input) by a monolingual parser or a tree-based translation system (e.g., tree to...

We present the first streaming algorithm for counting an arbitrary hypergraph H of constant size in a massive hypergraph G. Our algorithm can handle both edge-insertions and edge-deletions, and is applicable for the distributed setting. Moreover, our approach provides the first family of graph polynomials for the hypergraph counting problem. Because of the close relationship between hypergraphs...

Hypergraph multiway cut problem is a problem of finding a minimum capacity set of hyperedges whose removal divides a given hypergraph into a specified number of connected components. We present an algorithm for this problem which runs in strongly polynomial-time if both the specified number of connected components and the maximum size of hyperedges in the hypergraph are constants. Our algorithm...