Binary treehyperbolic geometryMobius groupsemigroups of transformationsgeodesicsCalkin–Wilf treeLet D0 := {x + iy |x, y > 0}, and let (L, R) be a pair of M¨obius transformations corresponding to SL2(N0) matrices such that R(D0) and L(D0) are disjoint. Given such a pair (called...
Ruskey, F. "Information on Rooted Trees." http://www.theory.csc.uvic.ca/~cos/inf/tree/RootedTree.html.Sloane, N. J. A. Sequences A000081/M1180 and A051491 in "The On-Line Encyclopedia of Integer Sequences."Wilf, H. S. Combinatorial Algorithms: An Update. Philadelphia, PA: SIAM,...
In this chapter, we explained the features of rooted and unrooted trees, based on their structures and applications. Rooted trees provide a hierarchical model that is ideal for situations where organization and levels matter. We also understood how unrooted trees are effective in scenarios without a...
(cell event). the goal is to compare developmental trees. in the language of graph theory, we need to define a metric on the space of rooted unordered trees with possibly repeated labels. each tree has a root vertex, and each vertex has a label that is not necessarily unique. all vertic...
Aphylogenetic treeis a binary, rooted, unordered tree whose leaves are distinctly labeled. Aphylogenetic networkis a generalization of a phylogenetic tree formally defined as a rooted, connected, directed acyclic graph in which (1) each node has outdegree at most 2; (2) each node has indegree...
Together with the Conflict Packing technique, a key ingredient in our proofs is the notion of safe partition introduced in [6]. Next, we use the Conflict Packing technique and adapt the notion of safe partition to the context of trees to obtain a linear vertex-kernel for the k-dense-RTI ...
Given such a pair (called a left-right pair), we can construct a directed graph F (L, R) with vertices D-0 and edges {(z, L(z))} (z is an element of D0) boolean OR {(z, R(z))} (z is an element of D0), which is a collection of infinite binary trees. We a...
In this article, we propose new MDC formulations for the cases where the gene trees are unrooted/binary, rooted/non-binary, and unrooted/non-binary. Further, we prove structural theorems that allow us to extend the algorithms for the rooted/binary gene tree case to these cases in a ...
A. Khorunzhy, Sparse random matrices: spectral edge and statistics of rooted trees, Adv. in Appl. Probab., 33 (2001) 1-18.Khorunzhy, A. (2001) Sparse Random Matrices: Spectral Edge and Statistics of Rooted Trees, Advances in Applied Probability 33 (1) pp. 124-140....
New strahler numbers for rooted plane trees - Auber, Delest, et al. - 2004 () Citation Context ...t has been extended to unary–binary trees [5]. Various papers about the register function (or Horton–Strahler numbers) have been written; we cite a few here [2, 9, 15, 13, 11]....