Related papers: On full Souslin trees
We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed for…
We say two spanning trees of a graph are completely independent if their edge sets are disjoint, and for each pair of vertices, the paths between them in each spanning tree do not have any other vertex in common. Pai and Chang constructed…
In this paper we examine the classes of graphs whose $K_n$-complements are trees and quasi-threshold graphs and derive formulas for their number of spanning trees; for a subgraph $H$ of $K_n$, the $K_n$-complement of $H$ is the graph…
We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
We present some exact expressions for the number of paths of a given length in a perfect $m$-ary tree. We first count the paths in perfect rooted $m$-ary trees and then use the results to determine the number of paths in perfect unrooted…
We consider the rooted trees which not have isomorphic representation and introduce a conception of complexity a natural number also. The connection between quantity such trees with $n$ edges and a complexity of natural number $n$ is…
We prove that if the normal distribution of a singular riemannian foliation is integrable, then each leaf of this normal distribution can be extended to be a complete immersed totally geodesic submanifold (called section) which meets every…
Given a set of colored points in the plane, we ask if there exists a crossing-free straight-line drawing of a spanning forest, such that every tree in the forest contains exactly the points of one color class. We show that the problem is…
We generalize Schwenk's result that almost all trees contain any given limb to trees with positive integer vertex weights. The concept of characteristic polynomial is extended to such weighted trees and we prove that the proportion of…
In this paper we analyse some questions concerning trees on $\kappa$, both for the countable and the uncountable case, and the connections with Cohen reals. In particular, we provide a proof for one of the implications left open in…
In this note, we prove two supercongruences involving Almkvist--Zudilin sequences, which were originally conjectured by Z.-H. Sun.
Disjoint-Set forests, consisting of Union-Find trees are data structures having a widespread practical application due to their efficiency. Despite them being well-known, no exact structural characterization of these trees is known (such a…
By analogy with the classical (Chasles-Schubert-Semple-Tyrell) spaces of complete quadrics and complete collineations, we introduce the variety of complete complexes. Its points can be seen as equivalence classes of spectral sequences of a…
Several variants of the Halpern-L\"auchli Theorem for trees of uncountable height are investigated. For $\kappa$ weakly compact, we prove that the various statements are all equivalent. We show that the strong tree version holds for one…
Assuming Jensen's principle diamond-plus we construct Souslin algebras all of whose maximal chains are pairwise isomorphic as total orders, thereby answering questions of Koppelberg and Todorcevic
We prove that every simple polygon contains a degree 3 tree encompassing a prescribed set of vertices. We give tight bounds on the minimal number of degree 3 vertices. We apply this result to reprove a result from Bose et al. that every set…
We establish a sharp sufficient condition for groups acting on trees to be highly transitive when the action on the tree is minimal of general type. This gives new examples of highly transitive groups, including icc non-solvable…
It implicitly follows from the work of [Colbourn, El-Mallah: On two dual classes of planar graphs. Discrete Mathematics 80(1): 21-40 (1990)] that every planar partial 3-tree is a subgraph of a planar 3-tree. This fact has already enabled to…
We study various types of consistency of honest decision trees and random forests in the regression setting. In contrast to related literature, our proofs are elementary and follow the classical arguments used for smoothing methods. Under…
Building upon work of L\"{u}cke and Schlicht, we study (higher) Kurepa trees through the lens of higher descriptive set theory, focusing in particular on various perfect set properties and representations of sets of branches through trees…