The union of two disjoint (n, 4n−1, 2) MDS codes in {0, 1, 2, 3}n is a double-MDS-code. If the adjacency graph of the double-MDS-code is not connected, then the double-code can be decomposed into double-MDS-codes of smaller lengths. If the graph has more than two connected components, then the MDS codes are also decomposable. The result has an interpretation in terms of n-quasigroups of order 4...

We define the character sheaves on a connected component of a reductive group and we show that the restriction functor takes a character sheaf to a direct sum of character sheaves.

Abstract. We consider a finite number of particles initially close to spherical but of varying size exhibiting the property of preserving the measure of each connected component. We show that under the assumptions i) particle size/interparticle distance 1 and ii) initial deviation from sphericity/particle size 1 the particles retain their almost spherical shape and the dynamics of the system is...

We completely describe the structure of the connected components of transversals to a collection of n line segments in R. Generically, the set of transversal to four segments consist of zero or two lines. We catalog the non-generic cases and show that n > 3 arbitrary line segments in R admit at most n connected components of line transversals, and that this bound can be achieved in certain conf...

The relationship between graph coloring and the immersion order is considered. Vertex connectivity, edge connectivity and related issues are explored. It is shown that a t-chromatic graph G contains either an immersed Kt or an immersed t-chromatic subgraph that is both 4-vertex-connected and t-edge-connected. This gives supporting evidence of our conjecture that if G requires at least t colors,...

Krishnamoorthy, Thulasiraman and Swamy [Minimum order graphs with specified diameter, connectivity and regularity, Networks 19 (1989) 25–46] showed that a δ-regular graph with diameter D at most 3 has (vertex-)connectivity κ at least 2, and if D ≤ 2 then the connectivity is at least κ ≥ min{δ, 3}. Likewise, Soneoka, Nakada, Imase and Peyrat [Sufficient conditions for maximally connected graphs,...

This paper proposes a method for detecting copy-move forgery over images tampered by copying some regions and pasting them onto other regions. To detect those forgeries, we divide the given image into overlapping blocks, extract feature for each blocks, and sort the extracted feature vectors by radix sort. The difference (shift vector) of the coordinates of every pair of adjacent vectors in the...

We consider high-order connectivity in k-uniform hypergraphs defined as follows: Two j-sets are j-connected if there is a walk of edges between them such that two consecutive edges intersect in at least j vertices. We describe the evolution of jconnected components in the k-uniform binomial random hypergraph H(n, p). In particular, we determine the asymptotic size of the giant component shortly...

A subset T ⊆ V of terminals is k-connected to a root s in a directed/undirected graph J if J has k internally-disjoint vs-paths for every v ∈ T ; T is k-connected in J if T is k-connected to every s ∈ T . We consider the Subset k-Connectivity Augmentation problem: given a graph G = (V,E) with edge/node-costs, node subset T ⊆ V , and a subgraph J = (V,EJ ) of G such that T is k-connected in J , ...

Vertex and edge connectivity are special cases of mixed connectivity, in which all edges and a specified set of vertices play a similar role. Certificates of k-connectivity for a graph are obtained by removing a subset of its edges, while preserving its connectivity up to k. We unify the previous work on connectivity certificates and extend it to handle mixed connectivity and multigraphs. Our t...