Related papers: On the local profiles of trees
We determine the tree which maximizes the distance between characteristic set and subtree core over all trees on $n$ vertices. The asymptotic nature of this distance is also discussed. The problem of extremizing the distance between…
The properties of scale-free random trees are investigated using both preconditioning on non-extinction and fixed size averages, in order to study the thermodynamic limit. The scaling form of volume probability is found, the connectivity…
The goal of these lectures is to survey some of the recent progress on the description of large-scale structure of random trees. We use the framework of Markov-Branching sequences of trees and discuss several applications.
We provide an easily verifiable condition for local $k$-connectedness of an inverse limit of polyhedra.
We study the Steiner $k$-eccentricity on trees, which generalizes the previous one in the paper [X.~Li, G.~Yu, S.~Klav\v{z}ar, On the average Steiner 3-eccentricity of trees, arXiv:2005.10319, 2020]. To support the algorithm, we achieve…
An independent $[1,k]$-set $S$ in a graph $G$ is a dominating set which is independent and such that every vertex not in $S$ has at most $k$ neighbors in it. The existence of such sets is not guaranteed in every graph and trees having an…
We establish how a higher local field can be described as a locally convex vector space once an embedding of a local field into it has been fixed. This extends previous results that had been obtained in the two-dimensional case. In…
The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
We study the energy per vertex in regular graphs. For every k, we give an upper bound for the energy per vertex of a k-regular graph, and show that a graph attains the upper bound if and only if it is the disjoint union of incidence graphs…
Let $X$ be an algebraic variety over a field $K \subset \overline{{\mathbb{Q}}_p}$ and $f$ be a self map. When $K$ is a local field, the boundedness of $f$-periods in $X(K)$ is a well studied question. We will study the same question for…
Phylogenetic trees are used to model evolution: leaves are labelled to represent contemporary species ("taxa") and interior vertices represent extinct ancestors. Informally, convex characters are measurements on the contemporary species in…
We construct finite sets of real numbers that have a small difference set and strong local properties. In particular, we construct a set $A$ of $n$ real numbers such that $|A-A|=n^{\log_2 3}$ and that every subset $A'\subseteq A$ of size…
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…
In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie…
Experts advising decision-makers are likely to display expertise which varies as a function of the problem instance. In practice, this may lead to sub-optimal or discriminatory decisions against minority cases. In this work we model such…
Recent research revealed the existence of gaps in the complexity landscape of locally checkable labeling (LCL) problems in the LOCAL model of distributed computing. For example, the deterministic round complexity of any LCL problem on…
Geometric embedding of graphs in a point set in the plane is a well known problem. In this paper, the complexity of a variant of this problem, where the point set is bounded by a simple polygon, is considered. Given a point set in the plane…
A rich line of work has been addressing the computational complexity of locally checkable labelings (LCLs), illustrating the landscape of possible complexities. In this paper, we study the landscape of LCL complexities under bandwidth…
We prove a local convex version of Arveson's extension theorem and of Wittstock's extension theorem. Also we prove a Stinespring type theorem for unbounded local completely contractive maps.