Related papers: Mal'cev conditions from graphs for congruences and…
Graph Laplacians on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of either $\delta$ or $\delta'$ type. In either case, an infinite series of trace formulae which…
We consider realizations of a graph in the plane such that the distances between adjacent vertices satisfy the constraints given by an edge labeling. If there are infinitely many such realizations, counted modulo rigid motions, the labeling…
We introduce a variation of interval graphs, called veto interval (VI) graphs. A VI graph is represented by a set of closed intervals, each containing a point called a veto mark. The edge $ab$ is in the graph if the intervals corresponding…
In this paper we address the graph matching problem. Following the recent works of \cite{zaslavskiy2009path,Vestner2017} we analyze and generalize the idea of concave relaxations. We introduce the concepts of conditionally concave and…
We explore the graph approach to contextuality to restate the extended definition of noncontextuality as given by J. Kujala et. al. [Phys. Rev. Lett. 115, 150401 (2015)] using graph-theoretical terms. This extended definition avoids the…
We show that, when restricted to the class of varieties that have a Taylor term, several commutator properties are definable by Maltsev conditions.
There are typically several nonisomorphic graphs having a given degree sequence, and for any two degree sequence terms it is often possible to find a realization in which the corresponding vertices are adjacent and one in which they are…
We examine spaces of connected tri-/univalent graphs subject to local relations which are motivated by the theory of Vassiliev invariants. It is shown that the behaviour of ladder-like subgraphs is strongly related to the parity of the…
Recent work of Lazarovich provides necessary and sufficient conditions on a graph L for there to exist a unique simply-connected (k,L)-complex. The two conditions are symmetry properties of the graph, namely star-transitivity and…
A matching in a graph is uniquely restricted if no other matching covers exactly the same set of vertices. We establish tight lower bounds on the maximum size of a uniquely restricted matching in terms of order, size, and maximum degree.
We study the graphs generated when the formula for linking Markov triples is applied to general triples of integers. We find there are a finite number of equivalence classes of graphs, each with particular properties.
In this paper, we continue the classification work done in the first paper of the same name. With careful modifications of our previous approach, we are able to deduce (with two notable exceptions) which members of the previously introduced…
We exploit a result by Nerman which shows that conditional limit theorems hold when a certain monotonicity condition is satisfied. Our main result is an application to vertex degrees in random graphs, where we obtain asymptotic normality…
Ancestral graphs can encode conditional independence relations that arise in directed acyclic graph (DAG) models with latent and selection variables. However, for any ancestral graph, there may be several other graphs to which it is Markov…
By counting the numbers of periodic points of all periods for some interval maps, we obtain infinitely many new congruence identities in number theory.
Graph Generating Dependencies (GGDs) informally express constraints between two (possibly different) graph patterns which enforce relationships on both graph's data (via property value constraints) and its structure (via topological…
In this article, we provide a new algorithm for solving constraint satisfaction problems with Maltsev constraints, based on the new notion of Maltsev consistency.
Graph colorings are becoming an increasingly useful family of mathematical models for a broad range of applications, such as time tabling and scheduling, frequency assignment, register allocation, computer security and so on. Graph proper…
Understanding causal relationships among the variables of a system is paramount to explain and control its behavior. For many real-world systems, however, the true causal graph is not readily available and one must resort to predictions…
We solve some problems about relative lengths of Maltsev conditions, in particular, we give an affirmative answer to a classical problem raised by A. Day more than fifty years ago. In detail, both congruence distributive and congruence…