A uniform approach to complexes arising from forests.
Addendum and erratum to the paper "On the size of a maximal induced tree in a random graph"
Additive functions on trees
The motivation for considering positive additive functions on trees was a characterization of extended Dynkin graphs (see I. Reiten [R]) and applications of additive functions in representation theory (see H. Lenzing and I. Reiten [LR] and T. Hübner [H]). We consider graphs equipped with integer-valued functions, i.e. valued graphs (see also [DR]). Methods are given for constructing additive functions on valued trees (in particular on Euclidean graphs) and for characterizing...
Algebraic approach to locally finite trees with one end
Let be an infinite locally finite tree. We say that has exactly one end, if in any two one-way infinite paths have a common rest (infinite subpath). The paper describes the structure of such trees and tries to formalize it by algebraic means, namely by means of acyclic monounary algebras or tree semilattices. In these algebraic structures the homomorpisms and direct products are considered and investigated with the aim of showing, whether they give algebras with the required properties. At...
Algebraic connectivity of trees
Algebraic properties of Husimi trees
Algorithm 88. A new algorithm calculating the distance between binary arborescences
Almost all trees have an even number of independent sets.
Almost every tree function is independent
An algorithmic Friedman-Pippenger theorem on tree embeddings and applications.
An anti-Ramsey condition on trees.
An Application of Circuit Polynomials to the Counting of Spanning Trees in Graphs
An identity for the independence polynomials of trees.
An inequality chain of domination parameters for trees
We prove that the smallest cardinality of a maximal packing in any tree is at most the cardinality of an R-annihilated set. As a corollary to this result we point out that a set of parameters of trees involving packing, perfect neighbourhood, R-annihilated, irredundant and dominating sets is totally ordered. The class of trees for which all these parameters are equal is described and we give an example of a tree in which most of them are distinct.
An Inversion Formula for the Radon Transform on Trees.
Analogies entre espaces hyperboliques réels et l’arbre de Bruhat-Tits sur
Analytic Formulas for Full Steiner Trees.
Analyzing sets of phylogenetic trees using metrics
The reconstruction of evolutionary trees is one of the primary objectives in phylogenetics. Such a tree represents historical evolutionary relationships between different species or organisms. Tree comparisons are used for multiple purposes, from unveiling the history of species to deciphering evolutionary associations among organisms and geographical areas. In this paper, we describe a general method for comparing phylogenetic trees and give some basic properties of the Matching Split metric, which...
Approximation des dissimilarités par des arbres additifs
Arbology: Trees and pushdown automata
We present a unified and systematic approach to basic principles of Arbology, a new algorithmic discipline focusing on algorithms on trees. Stringology, a highly developed algorithmic discipline in the area of string processing, can use finite automata as its basic model of computation. For various kinds of linear notations of ranked and unranked ordered trees it holds that subtrees of a tree in a linear notation are substrings of the tree in the linear notation. Arbology uses pushdown automata...