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This paper presents a novel theoretical Monte Carlo Markov chain procedure in the framework of graphs. It specifically deals with the construction of a Markov chain whose empirical distribution converges to a given reference one. The Markov…
For minimally rigid graphs, the same edge-length data can admit multiple realizations (up to translations and rotations). Finding graphs with exceptionally many realizations is an extremal problem in rigidity theory, but exhaustive search…
We study limits of convergent sequences of string graphs, that is, graphs with an intersection representation consisting of curves in the plane. We use these results to study the limiting behavior of a sequence of random string graphs. We…
The main goal of this paper is to formalize and explore a connection between chromatic properties of graphs with geometric representations and competitive analysis of on-line algorithms, which became apparent after the recent construction…
Graph comparison is fundamentally important for many applications such as the analysis of social networks and biological data and has been a significant research area in the pattern recognition and pattern analysis domains. Nowadays, the…
Estimating the number of subgraphs in data streams is a fundamental problem that has received great attention in the past decade. In this paper, we give improved streaming algorithms for approximately counting the number of occurrences of…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…
The concept of graph compositions is related to several number theoretic concepts, including partitions of positive integers and the cardinality of the power set of finite sets. This paper examines graph compositions where the total number…
Verifying the veracity of claims requires reasoning over a large knowledge base, often in the form of corpora of trustworthy sources. A common approach consists in retrieving short portions of relevant text from the reference documents and…
Joint time-vertex graph signals are pervasive in real-world. This paper focuses on the fundamental problem of sampling and reconstruction of joint time-vertex graph signals. We prove the existence and the necessary condition of a critical…
We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the sum with respect to…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
Consider a random graph model where each possible edge $e$ is present independently with some probability $p_e$. Given these probabilities, we want to build a large/heavy matching in the randomly generated graph. However, the only way we…
We propose an algorithm to estimate the topology of an embedded metric graph from a well-sampled finite subset of the underlying graph.
We propose a universal approach to a range of enumeration problems in graphs. The key point is in contracting suitably chosen symmetric tensors placed at the vertices of a graph along the edges. In particular, this leads to an algorithm…
The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of a…
In a digraph with $n$ vertices, a minuscule construct is a subdigraph with $m<<n$ vertices. We study the number of copies of a minuscule constructs in $k$ nearest neighbor ($k$NN) digraph of the data from a random point process in…
Determining the number of embeddings of Laman graph frameworks is an open problem which corresponds to understanding the solutions of the resulting systems of equations. In this paper we investigate the bounds which can be obtained from the…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…