Related papers: Parameter testing with bounded degree graphs of su…
Distribution testing deals with what information can be deduced about an unknown distribution over $\{1,\ldots,n\}$, where the algorithm is only allowed to obtain a relatively small number of independent samples from the distribution. In…
An assignment of colours to the vertices of a graph is stable if any two vertices of the same colour have identically coloured neighbourhoods. The goal of colour refinement is to find a stable colouring that uses a minimum number of…
The diameter, radius and eccentricities are natural graph parameters. While these problems have been studied extensively, there are no known dynamic algorithms for them beyond the ones that follow from trivial recomputation after each…
Metric dimension is a graph parameter motivated by problems in robot navigation, drug design, and image processing. In this paper, we answer several open extremal problems on metric dimension and pattern avoidance in graphs from (Geneson,…
Colored graphical models provide a parsimonious approach to modeling high-dimensional data by exploiting symmetries in the model parameters. In this work, we introduce the notion of coloring for extremal graphical models on multivariate…
We present the implementation of an algorithm for graph isomorphism testing, based on ideas about number of walks (of sufficiently large length) between vertices. The algorithm is expanded for strongly regular graphs (SRG-s) by testing the…
We resolve a number of long-standing open problems in online graph coloring. More specifically, we develop tight lower bounds on the performance of online algorithms for fundamental graph classes. An important contribution is that our…
Structural properties of large random maps and lambda-terms may be gleaned by studying the limit distributions of various parameters of interest. In our work we focus on restricted classes of maps and their counterparts in the…
Background modelling is one of the main challenges in particle physics data analysis. Commonly employed strategies include the use of simulated events of the background processes, and the fitting of parametric background models to the…
We show a method how to convert any graph into the binary number and vice versa. We derive upper bound for maximum number of graphs, that, have fixed number of vertices and can be colored with n colors (n is any given number). Proof for the…
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…
We examine maximum vertex coloring of random geometric graphs, in an arbitrary but fixed dimension, with a constant number of colors. Since this problem is neither scale-invariant nor smooth, the usual methodology to obtain limit laws…
In this paper we present distributed testing algorithms of graph properties in the CONGEST-model [Censor-Hillel et al. 2016]. We present one-sided error testing algorithms in the general graph model. We first describe a general procedure…
Consider a graph $G$ drawn on a fixed surface, and assign to each vertex a list of colors of size at least two if $G$ is triangle-free and at least three otherwise. We prove that we can give each vertex a color from its list so that each…
Let $G$ be a graph such that each vertex has its list of available colors, and assume that each list is a subset of the common set consisting of $k$ colors. For two given list colorings of $G$, we study the problem of transforming one into…
We consider properties of edge-colored vertex-ordered graphs, i.e., graphs with a totally ordered vertex set and a finite set of possible edge colors. We show that any hereditary property of such graphs is strongly testable, i.e., testable…
We claimed that there is a polynomial algorithm to test if two graphs are isomorphic. But the algorithm is wrong. It only tests if the adjacency matrices of two graphs have the same eigenvalues. There is a counterexample of two…
We argue that the vulnerability of model parameters is of crucial value to the study of model robustness and generalization but little research has been devoted to understanding this matter. In this work, we propose an indicator to measure…
Understanding causal relationships between variables is a fundamental problem with broad impact in numerous scientific fields. While extensive research has been dedicated to learning causal graphs from data, its complementary concept of…
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…