相关论文: Specializing Aronszajn trees by countable approxim…
Elementary arguments show that a tree or forest is determined (up to isomorphism) by binary matroids defined using the adjacency matrix.
For $f,g\in\omega^\omega$ let $c^\forall_{f,g}$ be the minimal number of uniform $g$-splitting trees needed to cover the uniform $f$-splitting tree, i.e., for every branch $\nu$ of the $f$-tree, one of the $g$-trees contains $\nu$. Let…
We study effective randomness-preserving transformations of path-incompressible trees. Some path-incompressible trees with infinitely many paths do not compute perfect path-random trees with computable oracle-use. Sparse perfect…
In this article it is shown that the Brownian motion on the continuum random tree is the scaling limit of the simple random walks on any family of discrete $n$-vertex ordered graph trees whose search-depth functions converge to the Brownian…
We isolate a combinatorial property of capacities leading to a construction of proper forcings. Then we show that many classical capacities such as the Newtonian capacity satisfy the property.
We consider large uniform random trees where we fix for each vertex its degree and height. We prove, under natural conditions of convergence for the profile, that those trees properly renormalized converge. To this end, we study the paths…
We characterize countable dimensionality and strong countable dimensionality by means of an infinite game.
We define some new sequences of recursively constructed random combinatorial trees, and show that, after properly rescaling graph distance and equipping the trees with the uniform measure on vertices, each sequence converges almost surely…
The strength of an extension of Kruskal's Theorem to certain pairs of cohabitation trees is calibrated.
Quasi-trees generalize trees in that the unique "path" between two nodes may be infinite and have any countable order type. They are used to define the rank-width of a countable graph in such a way that it is equal to the least upper-bound…
We present an approximation algorithm for Weighted Tree Augmentation with approximation factor $1+\ln 2 + \varepsilon < 1.7$. This is the first algorithm beating the longstanding factor of $2$, which can be achieved through many standard…
We characterize the extremal trees that maximize the number of almost-perfect matchings, which are matchings covering all but one or two vertices, and those that maximize the number of strong almost-perfect matchings, which are matchings…
We prove that if there exists a simplified $(\omega_1,2)$-morass, then there is a ccc forcing which adds an $\omega_3$-chain in P($\omega_1$) mod finite and a ccc forcing which adds a family of $\omega_3$-many strongly almost disjoint…
In this paper we aim to compare Kurepa trees and Aronszajn trees. Moreover, we analyze the affect of large cardinal assumptions on this comparison. Using the the method of walks on ordinals, we will show it is consistent with ZFC that there…
We prove that there are groups in the constructible universe whose automorphism towers are highly malleable by forcing. This is a consequence of the fact that, under a suitable diamond hypothesis, there are sufficiently many highly rigid…
This paper investigates the a-posteriori analysis of Branch-and-Bound~(BB) trees to extract structural information about the feasible region of mixed-binary linear programs. We introduce three novel outer approximations of the feasible…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
We define and prove isomorphisms between three combinatorial classes involving labeled trees. We also give an alternative proof by means of generating functions.
The purpose of this article is to prove that the forcing axiom for completely proper forcings is inconsistent with the Continuum Hypothesis. This answers a longstanding problem of Shelah. The corresponding completely proper forcing which…
Counterfactual explanations elucidate algorithmic decisions by pointing to scenarios that would have led to an alternative, desired outcome. Giving insight into the model's behavior, they hint users towards possible actions and give grounds…