Related papers: Graphs and codes produced by a new method for divi…
In many statistical applications, the dimension is too large to handle for standard high-dimensional machine learning procedures. This is particularly true for graphical models, where the interpretation of a large graph is difficult and…
In this paper two cryptographic methods are introduced. In the first method the presence of a certain size subgroup of persons can be checked for an action to take place. For this we use fragments of Raptor codes delivered to the group…
We describe and axiomatize finite solitaire puzzles and zero sum sequential games graph theoretically. Zermelo's theorem telling that there is a win for one of the players or a draw follows from the definitions. The god number is a…
In this paper, we consider a game played on a rectangular $m \times n$ gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of taking any piece of chocolate and breaking it again along…
The Szemer\'edi Regularity Lemma, in combination with the Blow-up Lemma, form the Regularity Method, a fundamental tool in graph embeddings, albeit restricted to very large and dense graphs. We propose an alternative vertex-partitioning…
In this paper, we present a hybrid graph-drawing algorithm (GDA) for layouting large, naturally-clustered, disconnected graphs. We called it a hybrid algorithm because it is an implementation of a series of already known graph-drawing and…
This introduction to graphs and graph algebras provides the optimal bound for the number of all paths of length $k$ in a graph with $N\geq k$ edges and no loops. Our proof relies on a construction of a number of terminating algorithms that…
Classical coding theory contains several techniques to obtain new codes from other codes, including puncturing and shortening. For quantum codes, a form of puncturing is known, but its description is based on the code space rather than its…
Let $G=(V,E)$ be a simple connected graph. A matching of $G$ is a set of disjoint edges of $G$. For every $n, m\in\mathbb{N}$, the $n$-subdivision of $G$ is a simple graph $G^{\frac{1}{n}}$ which is constructed by replacing each edge of $G$…
We propose a new approach for defining and searching clusters in graphs that represent real technological or transaction networks. In contrast to the standard way of finding dense parts of a graph, we concentrate on the structure of edges…
While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
A module of a graph G is a set of vertices that have the same set of neighbours outside. Modules of a graphs form a so-called partitive family and thereby can be represented by a unique tree MD(G), called the modular decomposition tree.…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…
The guessing number of a directed graph (digraph), equivalent to the entropy of that digraph, was introduced as a direct criterion on the solvability of a network coding instance. This paper makes two contributions on the guessing number.…
We consider the secure computation problem in a minimal model, where Alice and Bob each holds an input and wish to securely compute a function of their inputs at Carol without revealing any additional information about the inputs. For this…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
This paper develops a fundamental theory of realizations of linear and group codes on general graphs using elementary group theory, including basic group duality theory. Principal new and extended results include: normal realization…
We present a new algorithm to explore or count the numerical semigroups of a given genus which uses the unleaved version of the tree of numerical semigroups. In the unleaved tree there are no leaves rather than the ones at depth equal to…
Given a sufficiently large and sufficiently dense bipartite graph $G=(A, B; E),$ we present a novel method for decomposing the majority of the edges of $G$ into quasirandom graphs so that the vertex sets of these quasirandom graphs…
In this brief paper, a simple and fast computational method, the Planar Visibility Graph Networks Algorithm was proposed based on the famous Visibility Graph Algorithm, which can fulfill converting two dimensional timeseries into a planar…