相关论文: The Length of a Minimal Tree With a Given Topology…

In the longest plane spanning tree problem, we are given a finite planar point set $\mathcal{P}$, and our task is to find a plane (i.e., noncrossing) spanning tree for $\mathcal{P}$ with maximum total Euclidean edge length. Despite more…

This article studies the limit of binary search trees drawn from Mallows permutations under various topologies. The main result, pertaining to the standard local topology for graphs, requires the introduction of a generalization of binary…

We investigate the statistics of extremal path(s) (both the shortest and the longest) from the root to the bottom of a Cayley tree. The lengths of the edges are assumed to be independent identically distributed random variables drawn from a…

A tree T_uni is m-universal for the class of trees if for every tree T of size m, T can be obtained from T_uni by successive contractions of edges. We prove that a m-universal tree for the class of trees has at least mln(m) + (gamma-1)m +…

Tropical geometry with the max-plus algebra has been applied to statistical learning models over tree spaces because geometry with the tropical metric over tree spaces has some nice properties such as convexity in terms of the tropical…

We investigate extremal statistical properties such as the maximal and the minimal heights of randomly generated binary trees. By analyzing the master evolution equations we show that the cumulative distribution of extremal heights…

Comparing and computing distances between phylogenetic trees are important biological problems, especially for models where edge lengths play an important role. The geodesic distance measure between two phylogenetic trees with edge lengths…

We study planar straight-line drawings of graphs that minimize the ratio between the length of the longest and the shortest edge. We answer a question of Lazard et al. [Theor. Comput. Sci. 770 (2019), 88--94] and, for any given constant…

In this paper, we study how to draw trees so that they are planar, straight-line and respect a given order of edges around each node. We focus on minimizing the height, and show that we can always achieve a height of at most 2pw(T)+1, where…

We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.

A fundamental problem in network science is the normalization of the topological or physical distance between vertices, that requires understanding the range of variation of the unnormalized distances. Here we investigate the limits of the…

An approximate Steiner tree is a Steiner tree on a given set of terminals in Euclidean space such that the angles at the Steiner points are within a specified error e from 120 degrees.This notion arises in numerical approximations of…

A linear arrangement is a mapping $\pi$ from the $n$ vertices of a graph $G$ to $n$ distinct consecutive integers. Linear arrangements can be represented by drawing the vertices along a horizontal line and drawing the edges as semicircles…

In the present paper we show how one can calculate the lengths of edges of a minimum spanning tree constructed for a finite metric space, in terms of the Gromov-Hausdorff distances from this space to simplices of sufficiently large…

The treewidth of a graph is an important invariant in structural and algorithmic graph theory. This paper studies the treewidth of line graphs. We show that determining the treewidth of the line graph of a graph $G$ is equivalent to…

Maxmin trees are trees that consist of nodes that are either local minimums or maximums. Such trees were first studied by Postnikov. Later Dugan, Glennon, Gunnells, and Steingrimsson introduced the concept of weight to these trees and…

Maximum parsimony distance is a measure used to quantify the dissimilarity of two unrooted phylogenetic trees. It is NP-hard to compute, and very few positive algorithmic results are known due to its complex combinatorial structure. Here we…

A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a tree for every finite set of endpoints in…

We determine the maximum distance between any two of the center, centroid, and subtree core among trees with a given order. Corresponding results are obtained for trees with given maximum degree and also for trees with given diameter. The…

Minimal spanning trees on infinite vertex sets are investigated. A criterion for minimality of a spanning tree having a finite length is obtained, which generalizes the corresponding classical result for finite sets. It is given an analytic…