Related papers: Mixed Covering Arrays on 3-Uniform Hypergraphs
A $k$-uniform hypergraph $M$ is set-homogeneous if it is countable (possibly finite) and whenever two finite induced subhypergraphs $U,V$ are isomorphic there is $g\in Aut(M)$ with $U^g=V$; the hypergraph $M$ is said to be homogeneous if in…
An Euler tour in a hypergraph (also called a rank-2 universal cycle or 1-overlap cycle in the context of designs) is a closed walk that traverses every edge exactly once. In this paper, we define a covering $k$-hypergraph to be a non-empty…
Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…
We study thresholds for the appearance of a 2-core in random hypergraphs that are a mixture of a constant number of random uniform hypergraphs each with a linear number of edges but with different edge sizes. For the case of two overlapping…
The modeling flexibility provided by hypergraphs has drawn a lot of interest from the combinatorial scientific community, leading to novel models and algorithms, their applications, and development of associated tools. Hypergraphs are now a…
Let $G$ be a graph and let $J=I_c(G)$ be its ideal of covers. The aims of this work are to study the {\rm v}-number ${\rm v}(J)$ of $J$ and to study when $J$ is linearly presented using combinatorics and commutative algebra. We classify…
The aim of this paper is to generalize the notion of the coloring complex of a graph to hypergraphs. We present three different interpretations of those complexes -- a purely combinatorial one and two geometric ones. It is shown, that most…
Modern software systems often consist of many different components, each with a number of options. Although unit tests may reveal faulty options for individual components, functionally correct components may interact in unforeseen ways to…
Given a $k$-uniform hyper-graph, the E$k$-Vertex-Cover problem is to find the smallest subset of vertices that intersects every hyper-edge. We present a new multilayered PCP construction that extends the Raz verifier. This enables us to…
The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…
The best merge problem in industrial data science generates instances where disparate data sources place incompatible relational structures on the same set $V$ of objects. Graph vertex labelling data may include (1) missing or erroneous…
This paper deals with three graph characteristics related to graph covering named the (vertex, edge, and total, resp.) H-irregularity strength of a graph G admitting H-covering. Those are the minimum values of positive integer k such that G…
Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…
For each of the notions of hypergraph quasirandomness that have been studied, we identify a large class of hypergraphs F so that every quasirandom hypergraph H admits a perfect F-packing. An informal statement of a special case of our…
A linearly ordered (LO) $k$-colouring of an $r$-uniform hypergraph assigns an integer from $\{1, \ldots, k \}$ to every vertex so that, in every edge, the (multi)set of colours has a unique maximum. Equivalently, for $r=3$, if two vertices…
A covering array CA(N; t; k; v) is an N x k array on v symbols such that every N x t subarray contains as a row each t-tuple over the v symbols at least once. The minimum N for which a CA(N; t; k; v) exists is called the covering array…
A perfect matching in a hypergraph is a set of edges that partition the set of vertices. We study the complexity of deciding the existence of a perfect matching in orderable and separable hypergraphs. We show that the class of orderable…
A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For…
Let $n,s,k$ be three positive integers such that $1\leq s\leq(n-k+1)/k$ and let $[n]=\{1,\ldots,n\}$. Let $H$ be a $k$-graph with vertex set $\{1,\ldots,n\}$, and let $e(H)$ denote the number of edges of $H$. Let $\nu(H)$ and $\tau(H)$…
A connected digraph in which the in-degree of any vertex equals its out-degree is Eulerian; this baseline result is used as the basis of existence proofs for universal cycles (also known as ucycles or generalized deBruijn cycles or…