Related papers: Some probabilistic trees with algebraic roots
We study isomorphism invariant point processes of $\mathbb{R}^d$ whose groups of symmetries are almost surely trivial. We define a 1-ended, locally finite tree factor on the points of the process, that is, a mapping of the point…
Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning…
While the notion of arboricity of a graph is well-known in graph theory, very few results are dedicated to the minimal number of trees covering the edges of a graph, called the tree number of a graph.
In this note, we try to analyze and clarify the intriguing interplay between some counting problems related to specific thermalized weighted graphs and random walks consistent with such graphs.
We introduce and study a novel semi-random multigraph process, described as follows. The process starts with an empty graph on $n$ vertices. In every round of the process, one vertex $v$ of the graph is picked uniformly at random and…
Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of developing a theory of trees in higher dimension. As observed…
The family of trees with palindromic characteristic polynomials is characterized. Large families of graphs with this property are found as well.
We define an analytic version of the graph property testing problem, which can be formulated as studying an unknown 2-variable symmetric function through sampling from its domain and studying the random graph obtained when using the…
An intuitive property of a random graph is that its subgraphs should also appear randomly distributed. We consider graphs whose subgraph densities exactly match their expected values. We call graphs with this property for all subgraphs with…
A statistic can be a function of multiple samples. There is little existing work on asymptotic theory for such statistics when group membership is random. We propose a flexible framework that can handle both deterministic and random…
We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…
We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…
Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…
Tanglegrams are a special class of graphs appearing in applications concerning cospeciation and coevolution in biology and computer science. They are formed by identifying the leaves of two rooted binary trees. We give an explicit formula…
We examine the issue of stability of probability in reasoning about complex systems with uncertainty in structure. Normally, propositions are viewed as probability functions on an abstract random graph where it is implicitly assumed that…
We consider two varieties of labeled rooted trees, and the probability that a vertex chosen from all vertices of all trees of a given size uniformly at random has a given rank. We prove that this probability converges to a limit as the tree…
The Rabin tree theorem yields an algorithm to solve the satisfiability problem for monadic second-order logic over infinite trees. Here we solve the probabilistic variant of this problem. Namely, we show how to compute the probability that…
Stochastic branching processes are a classical model for describing random trees, which have applications in numerous fields including biology, physics, and natural language processing. In particular, they have recently been proposed to…