Related papers: Counting Bubbles in Linear Chord Diagrams
Consider two random strings having the same length and generated by an iid sequence taking its values uniformly in a fixed finite alphabet. Artificially place a long constant block into one of the strings, where a constant block is a…
A graph is a split graph if its vertex set can be partitioned into a clique and a stable set. A split graph is unbalanced if there exist two such partitions that are distinct. Cheng, Collins and Trenk (2016), discovered the following…
The objective of this study is to investigate the limiting behavior of a subgraph counting process. The subgraph counting process we consider counts the number of subgraphs having a specific shape that exist outside an expanding ball as the…
The radial distribution function is a characteristic geometric quantity of a point set in Euclidean space that reflects itself in the corresponding diffraction spectrum and related objects of physical interest. The underlying combinatorial…
This paper focuses on the modeling of musical melodies as networks. Notes of a melody can be treated as nodes of a network. Connections are created whenever notes are played in sequence. We analyze some main tracks coming from different…
In a finite undirected simple graph, a chordless cycle is an induced subgraph which is a cycle. A graph is called cyclically orientable if it admits an orientation in which every chordless cycle is cyclically oriented. We propose an…
Analytical expressions for the width and conductance peak distributions of irregularly shaped quantum dots in the Coulomb blockade regime are presented in the limits of conserved and broken time-reversal symmetry. The results are obtained…
A cycle cover of a graph is a collection of cycles such that each edge of the graph is contained in at least one of the cycles. The length of a cycle cover is the sum of all cycle lengths in the cover. We prove that every bridgeless cubic…
We consider large uniform labeled random graphs in different classes with prescribed decorations in their modular decomposition. Our main result is the estimation of the number of copies of every graph as an induced subgraph. As a…
The aim of this paper is to investigate the coupled oscillations of multiple bubbles within a cluster. The interaction between a bubble and the other bubbles in a cluster produces an additional mass. For a fixed number of bubbles ( ) and…
We present a method to estimate block membership of nodes in a random graph generated by a stochastic blockmodel. We use an embedding procedure motivated by the random dot product graph model, a particular example of the latent position…
Given a surface with boundary and some points on its boundary, a polygon diagram is a way to connect those points as vertices of non-overlapping polygons on the surface. Such polygon diagrams represent non-crossing permutations on a surface…
The simplest microfluidic network (a loop) comprises two parallel channels with a common inlet and a common outlet. Recent studies, that assumed constant cross-section of the channels along their length, have shown that the sequence of…
There is a simple and general experimental protocol to generate slow granular flows that exhibit wide shear zones, qualitatively different from the narrow shear bands that are usually observed in granular materials . The essence is to drive…
A graph is called chordal if it forbids induced cycles of length 4 or more. In this paper, we attempt to identify the non-nilpotent groups whose power graph is a chordal graph (this question was raised by Cameron in [4]). In this direction,…
The analysis of the size distribution of droplets condensing on a substrate (breath figures) is a test ground for scaling theories. Here, we show that a faithful description of these distributions must explicitly deal with the growth…
Bump hunting deals with finding in sample spaces meaningful data subsets known as bumps. These have traditionally been conceived as modal or concave regions in the graph of the underlying density function. We define an abstract bump…
The bandwidth of a graph G is the minimum of the maximum difference between adjacent labels when the vertices have distinct integer labels. We provide a polynomial algorithm to produce an optimal bandwidth labeling for graphs in a special…
A regular-graph design is a block design for which a pair $\{a,b\}$ of distinct points occurs in $\lambda+1$ or $\lambda$ blocks depending on whether $\{a,b\}$ is or is not an edge of a given $\delta$-regular graph. Our paper describes a…
Let $G$ be a graph with the usual shortest-path metric. A graph is $\delta$-hyperbolic if for every geodesic triangle $T$, any side of $T$ is contained in a $\delta$-neighborhood of the union of the other two sides. A graph is chordal if…