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Displaying similar documents to “From paths to stars.”

On the structure of path-like trees

F.A. Muntaner-Batle, Miquel Rius-Font (2008)

Discussiones Mathematicae Graph Theory

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We study the structure of path-like trees. In order to do this, we introduce a set of trees that we call expandable trees. In this paper we also generalize the concept of path-like trees and we call such generalization generalized path-like trees. As in the case of path-like trees, generalized path-like trees, have very nice labeling properties.

Characterization Results for theL(2, 1, 1)-Labeling Problem on Trees

Xiaoling Zhang, Kecai Deng (2017)

Discussiones Mathematicae Graph Theory

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An L(2, 1, 1)-labeling of a graph G is an assignment of non-negative integers (labels) to the vertices of G such that adjacent vertices receive labels with difference at least 2, and vertices at distance 2 or 3 receive distinct labels. The span of such a labelling is the difference between the maximum and minimum labels used, and the minimum span over all L(2, 1, 1)-labelings of G is called the L(2, 1, 1)-labeling number of G, denoted by λ2,1,1(G). It was shown by King, Ras and Zhou...

On a matching distance between rooted phylogenetic trees

Damian Bogdanowicz, Krzysztof Giaro (2013)

International Journal of Applied Mathematics and Computer Science

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The Robinson-Foulds (RF) distance is the most popular method of evaluating the dissimilarity between phylogenetic trees. In this paper, we define and explore in detail properties of the Matching Cluster (MC) distance, which can be regarded as a refinement of the RF metric for rooted trees. Similarly to RF, MC operates on clusters of compared trees, but the distance evaluation is more complex. Using the graph theoretic approach based on a minimum-weight perfect matching in bipartite graphs,...

The triangles method to build X -trees from incomplete distance matrices

Alain Guénoche, Bruno Leclerc (2001)

RAIRO - Operations Research - Recherche Opérationnelle

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A method to infer X -trees (valued trees having X as set of leaves) from incomplete distance arrays (where some entries are uncertain or unknown) is described. It allows us to build an unrooted tree using only 2 n -3 distance values between the n elements of X , if they fulfill some explicit conditions. This construction is based on the mapping between X -tree and a weighted generalized 2-tree spanning X .

Completely Independent Spanning Trees in (Partial) k-Trees

Masayoshi Matsushita, Yota Otachi, Toru Araki (2015)

Discussiones Mathematicae Graph Theory

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Two spanning trees T1 and T2 of a graph G are completely independent if, for any two vertices u and v, the paths from u to v in T1 and T2 are internally disjoint. For a graph G, we denote the maximum number of pairwise completely independent spanning trees by cist(G). In this paper, we consider cist(G) when G is a partial k-tree. First we show that [k/2] ≤ cist(G) ≤ k − 1 for any k-tree G. Then we show that for any p ∈ {[k/2], . . . , k − 1}, there exist infinitely many k-trees G such...

Small integral trees.

Brouwer, A.E. (2008)

The Electronic Journal of Combinatorics [electronic only]

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