Related papers: Non-crossing trees, quadrangular dissections, tern…

Let $G$ be an undirected simple connected graph. We say a vertex $u$ is eccentric to a vertex $v$ in $G$ if $d(u,v)=\max\{d(v,w): w\in V(G)\}$. The eccentric graph, $E(G)$ of $G$ is a graph defined on the same vertex set as of $G$ and two…

We show that there is a reflection type bijection between the indecomposable summands of two multiplicity free tilting modules $X$ and $Y$. This bijection fixes the common indecomposable summands of $X$ and $Y$ and sends indecomposable…

Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…

We introduce a notion of Dyck paths with coloured ascents. For several ways of colouring, we establish bijections between sets of such paths and other combinatorial structures, such as non-crossing trees, dissections of a convex polygon,…

In this paper, we investigate the problem of generating the spanning trees of a graph $G$ up to the automorphisms or "symmetries" of $G$. After introducing and surveying this problem for general input graphs, we present algorithms that…

In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered connection between the symmetric group and barcodes in general…

We give two combinatorial proofs of an elegant product formula for the number of spanning trees of the $n$-dimensional hypercube. The first proof is based on the assertion that if one chooses a uniformly random rooted spanning tree of the…

A connected graph can be associated with two distinct evolution algebras. In the first case, the structural matrix is the adjacency matrix of the graph itself. In the second case, the structural matrix is the transition probabilities matrix…

The search of spanning trees with interesting disjunction properties has led to the introduction of edge-disjoint spanning trees, independent spanning trees and more recently completely independent spanning trees. We group together these…

Rectangular layouts, subdivisions of an outer rectangle into smaller rectangles, have many applications in visualizing spatial information, for instance in rectangular cartograms in which the rectangles represent geographic or political…

Metabolites, small molecules that are involved in cellular reactions, provide a direct functional signature of cellular state. Untargeted metabolomics experiments usually relies on tandem mass spectrometry to identify the thousands of…

An edge-ordered graph is a graph with a total ordering of its edges. A path $P=v_1v_2\ldots v_k$ in an edge-ordered graph is called increasing if $(v_iv_{i+1}) > (v_{i+1}v_{i+2})$ for all $i = 1,\ldots,k-2$; it is called decreasing if…

We use the theory of \Gamma-species to enumerate k-gonal and polygonal 2-trees with respect to their vertices. We then extend this result to enumerate "succulents", a tree-like class of graphs which generalize cacti.

We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…

We revisit the twisted multiplicativity property of Voiculescu's S-transform in the operator-valued setting, using a specific bijection between planar binary trees and noncrossing partitions.

The early development of a zygote can be mathematically described by a developmental tree. To compare developmental trees of different species, we need to define distances on trees. If children cells after a division are not…

A piecewise constant curvature manifold is a triangulated manifold that is assigned a geometry by specifying lengths of edges and stipulating that for a chosen background geometry (Euclidean, hyperbolic, or spherical), each simplex has an…

In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…

A compacted binary tree is a graph created from a binary tree such that repeatedly occurring subtrees in the original tree are represented by pointers to existing ones, and hence every subtree is unique. Such representations form a special…

Recently the duality map between electric-like asymptotic charges of $p$-form gauge theories is studied. The outcome is an existence and uniqueness theorem and the topological nature of the duality map. The goal of this work is to extend…