Displaying similar documents to “An inequality chain of domination parameters for trees”

Generalizations of the tree packing conjecture

Dániel Gerbner, Balázs Keszegh, Cory Palmer (2012)

Discussiones Mathematicae Graph Theory

Similarity:

The Gyárfás tree packing conjecture asserts that any set of trees with 2,3,...,k vertices has an (edge-disjoint) packing into the complete graph on k vertices. Gyárfás and Lehel proved that the conjecture holds in some special cases. We address the problem of packing trees into k-chromatic graphs. In particular, we prove that if all but three of the trees are stars then they have a packing into any k-chromatic graph. We also consider several other generalizations of the conjecture. ...

On the packing of two copies of a caterpillar in its third power

Christian Germain, Hamamache Kheddouci (2003)

Discussiones Mathematicae Graph Theory

Similarity:

H. Kheddouci, J.F. Saclé and M. Woźniak conjectured in 2000 that if a tree T is not a star, then there is an edge-disjoint placement of T into its third power.In this paper, we prove the conjecture for caterpillars.

Carleson measures, trees, extrapolation, and T(b) theorems.

Pascal Auscher, Steve Hofmann, Camil Muscalu, Terence Tao, Christoph Thiele (2002)

Publicacions Matemàtiques

Similarity:

The theory of Carleson measures, stopping time arguments, and atomic decompositions has been well-established in harmonic analysis. More recent is the theory of phase space analysis from the point of view of wave packets on tiles, tree selection algorithms, and tree size estimates. The purpose of this paper is to demonstrate that the two theories are in fact closely related, by taking existing results and reproving them in a unified setting. In particular we give a dyadic version of...

A characterization of (γₜ,γ₂)-trees

You Lu, Xinmin Hou, Jun-Ming Xu, Ning Li (2010)

Discussiones Mathematicae Graph Theory

Similarity:

Let γₜ(G) and γ₂(G) be the total domination number and the 2-domination number of a graph G, respectively. It has been shown that: γₜ(T) ≤ γ₂(T) for any tree T. In this paper, we provide a constructive characterization of those trees with equal total domination number and 2-domination number.

Analyzing sets of phylogenetic trees using metrics

Damian Bogdanowicz (2011)

Applicationes Mathematicae

Similarity:

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...

Completely Independent Spanning Trees in (Partial) k-Trees

Masayoshi Matsushita, Yota Otachi, Toru Araki (2015)

Discussiones Mathematicae Graph Theory

Similarity:

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...

On A-Trees

Đuro Kurepa (1968)

Publications de l'Institut Mathématique

Similarity:

On a matching distance between rooted phylogenetic trees

Damian Bogdanowicz, Krzysztof Giaro (2013)

International Journal of Applied Mathematics and Computer Science

Similarity:

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,...