We prove that a k-uniform self-complementary hypergraph of order n exists, if and only if ( n k ) is even.

In ZF the existence of self-complementary graphs on every infinite set is equivalent to the statement that every infinite set is ’even’. We prove a generalization to k-uniform t-complementary hypergraphs. 1. Self-complementary graphs A graph G is called self-complementary if it is isomorphic to its complement G, which has the same vertices as G and exactly those edges that are not in G. First w...

A k-uniform hypergraph with vertex set V and edge set E is called t-subset-regular if every t-element subset of V lies in the same number of elements of E. In this paper we establish a necessary condition on n for there to exist a t-subset-regular selfcomplementary k-uniform hypergraph with n vertices. In addition, we show that this necessary condition is also sufficient in the case k = 3 and t...

In this paper we present fixed-parameter algorithms for the problem Dual—given two hypergraphs, decide if one is the transversal hypergraph of the other—and related problems. In the first part, we give algorithms for the parameters number of edges of the hypergraphs, the maximum degree of a vertex, and vertex complementary degrees. In the second part, we use an Apriori approach to obtain FPT re...

In this paper we present fixed-parameter algorithms for the problem Dual—given two hypergraphs, decide if one is the transversal hypergraph of the other—and related problems. In the first part, we consider the number of edges of the hypergraphs, the maximum degree of a vertex, and a vertex complementary degree as our parameters. In the second part, we use an Apriori approach to obtain FPT resul...

We show that a 2-subset-regular self-complementary 3-uniform hypergraph with n vertices exists if and only if n ≥ 6 and n is congruent to 2 modulo 4.

Individual differences in brain functional networks may be related to complex personal identifiers, including health, age, and ability. Dynamic network theory has been used to identify properties of dynamic brain function from fMRI data, but the majority of analyses and findings remain at the level of the group. Here, we apply hypergraph analysis, a method from dynamic network theory, to quanti...

In this thesis, we survey the current research into self-complementary hypergraphs, and present several new results. We characterize the cycle type of the permutations on n elements with order equal to a power of 2 which are k-complementing. The k-complementing permutations map the edges of a k-uniform hypergraph to the edges of its complement. This yields a test to determine whether a finite p...

Given a 3-uniform hypergraph H consisting of set V vertices, and T?V3 triples, null labelling is an assignment ±1 to the triples such that each vertex contained in equal number labelled +1 ?1. Thus, signed degree zero. A necessary condition for every even. The Null Labelling Problem determine whether has labelling. It proved this problem NP-complete. Computer enumerations suggest most hypergrap...

Diagram editors which are tailored to a specific diagram language typically support either syntax-directed editing or free-hand editing, i.e., the user is either restricted to a collection of predefined editing operations, or he is not restricted at all, but misses the convenience of such complex editing operations. This paper proposes a concept for incorporating both modes into one editor in o...