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.

In this paper, we show that the largest signless Laplacian H-eigenvalue of a connected k-uniform hypergraph G, where k ≥ 3, reaches its upper bound 2∆(G), where ∆(G) is the largest degree of G, if and only if G is regular. Thus the largest Laplacian H-eigenvalue of G, reaches the same upper bound, if and only if G is regular and oddbipartite. We show that an s-cycle G, as a k-uniform hypergraph...

Cross-modal remote sensing (RS) image retrieval aims to retrieve RS images using other modalities (e.g., text) and vice versa. The relationship between objects in the is complex, i.e., distribution of multiple types uneven, which makes matching with query text inaccurate, then restricts performance retrieval. Previous methods generally focus on feature rarely model relationships features image....

For a k-uniform hypergraph H, we obtain some trace formulas for the Laplacian tensor of H, which imply that ∑n i=1 d s i (s = 1, . . . , k) is determined by the Laplacian spectrum of H, where d1, . . . , dn is the degree sequence of H. Using trace formulas for the Laplacian tensor, we obtain expressions for some coefficients of the Laplacian polynomial of a regular hypergraph. We give some spec...

A set of edges of a hypergraph H is an algebraic set if its characteristic vector can be expressed as a linear combination of rows of the (node-edge) incidence matrix of H. Recently it was proven that deciding whether or not a given edge-set of H contains a non-empty algebraic set is an NP complete problem. In this paper we give a linear time algorithm to decide if a given edge-set contains a n...

This paper deals with an adaptation of the genetic partitioning algorithm BOA, based on the estimation of distribution of promising solution, for the placement of the hypergraph nodes into the regular structure of allocations. This task is a simplification of the placement problem encountered in PCB design or more complex case of physical layout of gate array on VLSI chip level. We present top-...

We establish an inclusion relation between two uniform models of random k-graphs (for constant k ≥ 2) on n labeled vertices: G(k)(n,m), the random k-graph with m edges, and R(k)(n, d), the random d-regular k-graph. We show that if n log n m nk we can choose d = d(n) ∼ km/n and couple G(k)(n,m) and R(k)(n, d) so that the latter contains the former with probability tending to one as n → ∞. This e...

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...

Diagrams that serve as a visual input facility for programming environments have to be translated into some kind of semantic description. This paper describes such a method which is based on a specification of the translation process. The translation process starts with a diagram, which is simply represented as a collection of atomic diagram components, and it ends up with some data structure a...

We develop the concept of weighted aligned hypergraph bimorphism where the weights may, in particular, represent probabilities. Such a bimorphism consists of an R≥0-weighted regular tree grammar, two hypergraph algebras that interpret the generated trees, and a family of alignments between the two interpretations. Semantically, this yields a set of bihypergraphs each consisting of two hypergrap...