Line minimal Boolean forests
Linear and metric maps on trees via Markov graphs
The main focus of combinatorial dynamics is put on the structure of periodic points (and the corresponding orbits) of topological dynamical systems. The first result in this area is the famous Sharkovsky's theorem which completely describes the coexistence of periods of periodic points for a continuous map from the closed unit interval to itself. One feature of this theorem is that it can be proved using digraphs of a special type (the so-called periodic graphs). In this paper we use Markov graphs...
Linear arboricity of graphs
Local admissible convergence of harmonic functions on non-homogeneous trees
We prove admissible convergence to the boundary of functions that are harmonic on a subset of a non-homogeneous tree equipped with a transition operator that satisfies uniform bounds suitable for transience. The approach is based on a discrete Green formula, suitable estimates for the Green and Poisson kernel and an analogue of the Lusin area function.
Local extrema in random trees.
Locally one-to-one mappings on graphs
Low-Degree Minimum Spanning Trees.
Lower bound on the distance -domination number of a tree
Lower bound on the domination number of a tree
>We prove that the domination number γ(T) of a tree T on n ≥ 3 vertices and with n₁ endvertices satisfies inequality γ(T) ≥ (n+2-n₁)/3 and we characterize the extremal graphs.
Lower bounds on signed edge total domination numbers in graphs
The open neighborhood of an edge in a graph is the set consisting of all edges having a common end-vertex with . Let be a function on , the edge set of , into the set . If for each , then is called a signed edge total dominating function of . The minimum of the values , taken over all signed edge total dominating function of , is called the signed edge total domination number of and is denoted by . Obviously, is defined only for graphs which have no connected components...
Mappings of Acyclic and Parking Functions.
Maximal buttonings of trees
A buttoning of a tree that has vertices v1, v2, . . . , vn is a closed walk that starts at v1 and travels along the shortest path in the tree to v2, and then along the shortest path to v3, and so forth, finishing with the shortest path from vn to v1. Inspired by a problem about buttoning a shirt inefficiently, we determine the maximum length of buttonings of trees
Maximum multiplicity of a root of the matching polynomial of a tree and minimum path cover.
Medians and peripherians of trees
Mesures de Gibbs sur les Cantor réguliers
Meta-Fibonacci sequences, binary trees and extremal compact codes.
Méthodes ordinales et combinatoires en analyse des données
Après quelques considérations générales sur les relations entre les mathématiques discrètes, l'informatique et l'analyse des données, ce texte présente un ensemble de méthodes utilisant des techniques ordinales ou (et) combinatoires. A une description succinte de chaque méthode sont jointes quelques références relatives à ses aspects théoriques ainsi qu'à ses implémentations accessibles aux utilisateurs. Pour présenter ces méthodes nous les avons classées suivant la nature des tableaux de données...
Metric dimension and zero forcing number of two families of line graphs
Zero forcing number has recently become an interesting graph parameter studied in its own right since its introduction by the “AIM Minimum Rank–Special Graphs Work Group”, whereas metric dimension is a well-known graph parameter. We investigate the metric dimension and the zero forcing number of some line graphs by first determining the metric dimension and the zero forcing number of the line graphs of wheel graphs and the bouquet of circles. We prove that for a simple and connected graph . Further,...
Metric spaces in pure and applied mathematics.
Minimal 2-dominating sets in trees
We provide an algorithm for listing all minimal 2-dominating sets of a tree of order n in time 𝒪(1.3248n). This implies that every tree has at most 1.3248n minimal 2-dominating sets. We also show that this bound is tight.