Related papers: On the local profiles of trees

We show that the cophylogenetic distance, k-interval cospeciation, is distinct from other metrics and accounts for global congruence between locally incongruent trees. The growth of the neighborhood of trees which satisfy the largest…

We give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations that are otherwise hard, for example, joint degree…

We compute the Coxeter polynomial of a family of Salem trees, and also the limit of the spectral radii of their Coxeter transformations as the number of their vertices tends to infinity. We also prove a relation about multiplicities of…

We prove a general multi-dimensional central limit theorem for the expected number of vertices of a given degree in the family of planar maps whose vertex degrees are restricted to an arbitrary (finite or infinite) set of positive integers…

We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…

This work will appear as a chapter in a forthcoming volume titled "Topics in Probabilistic Graph Theory". A theory of scaling limits for random graphs has been developed in recent years. This theory gives access to the large-scale geometric…

The concept of $k$-planarity is extensively studied in the context of Beyond Planarity. A graph is $k$-planar if it admits a drawing in the plane in which each edge is crossed at most $k$ times. The local crossing number of a graph is the…

For a k-tree T, a generalization of a tree, the local mean order of sub-k-trees of T is the average order of sub-k-trees of T containing a given k-clique. The problem whether the largest local mean order of a tree (i.e., a 1-tree) at a…

Piecewise linear vector optimization problems in a locally convex Hausdorff topological vector spaces setting are considered in this paper. The efficient solution set of these problems are shown to be the unions of finitely many semi-closed…

A graph drawn in the plane with straight-line edges is called a geometric graph. If no path of length at most $k$ in a geometric graph $G$ is self-intersecting we call $G$ $k$-locally plane. The main result of this paper is a construction…

While finite graphs have tree-decompositions that efficiently distinguish all their tangles, locally finite graphs with thick ends need not have such tree-decompositions. We show that every locally finite graph without thick ends admits…

Understanding the topology of sublevel sets yields crucial insights into the optimization landscape of non-convex functions. If sublevel sets are connected, local search algorithms are less likely to be trapped in isolated valleys,…

We study isometric actions of tree automorphism groups on the infinite-dimensional hyperbolic spaces. On the one hand, we exhibit a general one-parameter family of such representations and analyse the corresponding equivariant embeddings of…

We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…

We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a topological limit graphing.

We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…

Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…

This survey is devoted to discussing the problems of the unique determination of surfaces that are the boundaries of (generally speaking) nonconvex domains. First (in Sec. 2) we examine some results on the problem of the unique…

We systematically study a natural problem in extremal graph theory, to minimize the number of edges in a graph with a fixed number of vertices, subject to a certain local condition: each vertex must be in a copy of a fixed graph $H$. We…

A $k$-ranking of a graph $G$ is a labeling of its vertices from $\{1,\ldots,k\}$ such that any nontrivial path whose endpoints have the same label contains a larger label. The least $k$ for which $G$ has a $k$-ranking is the ranking number…