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On considère un graphe complet dont les arêtes sont totalement préordonnées. En analyse de similitude, plutôt que de procéder à un ordonnancement des arêtes ex oequo par une méthode lexicographique sur leurs intitulés, l'auteur propose de rechercher la réunion des arbres maximaux (RAM).

Les arbres et les indices de centralité et de compacité de P. Parlebas

B. Leclerc (1972)

Mathématiques et Sciences Humaines

Les hiérarchies de parties et leur demi-treillis

Bruno Leclerc (1985)

Mathématiques et Sciences Humaines

Limit distributions and random trees derived from the birthday problem with unequal probabilities.

Camarri, Michael, Pitman, Jim (2000)

Electronic Journal of Probability [electronic only]

Limit distributions for queues and random rooted trees.

Takács, Lajos (1993)

Journal of Applied Mathematics and Stochastic Analysis

Line minimal Boolean forests

Frank Harary, Abbe Mowshowitz, Allen Schwenk (1977)

Colloquium Mathematicae

Linear and metric maps on trees via Markov graphs

Sergiy Kozerenko (2018)

Commentationes Mathematicae Universitatis Carolinae

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

Mirosław Truszczyński (1986)

Mathematica Slovaca

Local admissible convergence of harmonic functions on non-homogeneous trees

Massimo A. Picardello (2010)

Colloquium Mathematicae

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.

Clark, Lane (2005)

International Journal of Mathematics and Mathematical Sciences

Locally one-to-one mappings on graphs

Janusz Jerzy Charatonik, Stanisław Miklos, Krzysztof Omiljanowski (1987)

Czechoslovak Mathematical Journal

Low-Degree Minimum Spanning Trees.

G. Robins, J.S. Salowe (1995)

Discrete & computational geometry

Lower bound on the distance $k$ -domination number of a tree

Joanna Raczek, Magdalena Lemańska, Joanna Cyman (2006)

Mathematica Slovaca

Lower bound on the domination number of a tree

Magdalena Lemańska (2004)

Discussiones Mathematicae Graph Theory

>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

H. Karami, S. M. Sheikholeslami, Abdollah Khodkar (2008)

Czechoslovak Mathematical Journal

The open neighborhood $N_{G} (e)$ of an edge $e$ in a graph $G$ is the set consisting of all edges having a common end-vertex with $e$ . Let $f$ be a function on $E (G)$ , the edge set of $G$ , into the set ${- 1, 1}$ . If $\sum_{x \in N_{G} (e)} f (x) \geq 1$ for each $e \in E (G)$ , then $f$ is called a signed edge total dominating function of $G$ . The minimum of the values $\sum_{e \in E (G)} f (e)$ , taken over all signed edge total dominating function $f$ of $G$ , is called the signed edge total domination number of $G$ and is denoted by $γ_{s t}^{'} (G)$ . Obviously, $γ_{s t}^{'} (G)$ is defined only for graphs $G$ which have no connected components...

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