Related papers: Injective Labeled Oriented Trees are Aspherical
If a graph has a non-singular adjacency matrix, then one may use the inverse matrix to define a (labeled) graph that may be considered to be the inverse graph to the original one. It has been known that an adjacency matrix of a tree is…
We construct a tree T of maximal degree 3 with infinitely many leaves such that whenever finitely many of them are removed, the remaining tree is isomorphic to T. In this sense T resembles an infinite star.
We consider graph labelings with an assignment of odd prime numbers to the vertices. Similarly to graceful graphs, a labeling is said to be elegant if the absolute differences between the labels of adjacent vertices describe exactly the…
In this thesis the properties of two kinds of non-uniform random recursive trees are studied. In the first model weights are assigned to each node, thus altering the attachment probabilities. We will call these trees weighted recursive…
Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…
A semi-lattice is said to be tree-like when any two of its elements are either orthogonal or comparable. Given an inverse semigroup S whose idempotent semi-lattice is tree-like, and such that all tight filters are ultra-filters, we present…
Assume that we embed the path $P_n$ as a subgraph of a $2$-dimensional grid, namely, $P_k \times P_l$. Given such an embedding, we consider the ordered set of subpaths $L_1, L_2, \ldots , L_m$ which are maximal straight segments in the…
We prove a strong form of the invariance under re-rooting of the distribution of the continuous random trees called Levy trees. This extends previous results due to several authors.
Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…
We prove that every amenable one-ended Cayley graph has an invariant spanning tree of one end. More generally, for any 1-ended amenable unimodular random graph we construct a factor of iid percolation (jointly unimodular subgraph) that is…
An evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species. Evolutionary trees are useful for modeling the evolutionary history of…
In this note, we classify all the weighted oriented forests whose edge ideals have the property that one of their matching powers has linear resolution.
We give a short proof of the fact that the number of labelled trees on $n$ vertices is $n^{n-2}$. Although many short proofs are known, we have not seen this one before.
Invariants for complicated objects such as those arising in phylogenetics, whether they are invariants as matrices, polynomials, or other mathematical structures, are important tools for distinguishing and working with such objects. In this…
We prove that the number of crossings in a random labelled tree with vertices in convex position is asymptotically Gaussian with mean $ n^2/6$ and variance $ n^3/45$. A similar result is proved for points in general position under mild…
The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…
A regular tree language L is locally testable if membership of a tree in L depends only on the presence or absence of some fix set of neighborhoods in the tree. In this paper we show that it is decidable whether a regular tree language is…
We introduce an encoding for parsing as sequence labeling that can represent any projective dependency tree as a sequence of 4-bit labels, one per word. The bits in each word's label represent (1) whether it is a right or left dependent,…
Semi-labeled trees are phylogenies whose internal nodes may be labeled by higher-order taxa. Thus, a leaf labeled Mus musculus could nest within a subtree whose root node is labeled Rodentia, which itself could nest within a subtree whose…