Related papers: The Partition Graph as a Growing Discrete Geometri…
Bottom-up approaches for image-based multi-person pose estimation consist of two stages: (1) keypoint detection and (2) grouping of the detected keypoints to form person instances. Current grouping approaches rely on learned embedding from…
For non-negative integers $(d_n(k))_{k \ge 1}$ such that $\sum_{k \ge 1} d_n(k) = n$, we sample a bipartite planar map with $n$ faces uniformly at random amongst those which have $d_n(k)$ faces of degree $2k$ for every $k \ge 1$ and we…
Given $k\ge 1$, a $k$-proper partition of a graph $G$ is a partition ${\mathcal P}$ of $V(G)$ such that each part $P$ of ${\mathcal P}$ induces a $k$-connected subgraph of $G$. We prove that if $G$ is a graph of order $n$ such that…
Due to the fact that the numbers of annually published papers have witnessed a linear growth in some citation networks, a geometric model is thus proposed to predict some statistical features of those networks, in which the academic…
Weight-equitable partitions of graphs, which are a natural extension of the well-known equitable partitions, have been shown to be a powerful tool to weaken the regularity assumption in several well-known eigenvalue bounds. In this work we…
Partitioning is a known problem in computer science and is critical in chip design workflows, as advancements in this area can significantly influence design quality and efficiency. Deep Learning (DL) techniques, particularly those…
We prove a full global Jacquet-Langlands correspondence between GL(n) and division algebras over global fields of non zero characteristic. If $D$ is a central division algebra of dimension $n^2$ over a global field $F$ of non zero…
In this note, we introduce a family of bipartite graphs called path restricted ordered bipartite graphs and present it as an abstract generalization of some well known geometric graphs like unit distance graphs on convex point sets. In the…
In this paper, we introduce a natural geometric extension of the partition function. More precisely, we investigate the problem of counting partitions of a rectangle into rectangular blocks with integer sides. Here, two partitions of a…
Image geolocalization is the task of identifying the location depicted in a photo based only on its visual information. This task is inherently challenging since many photos have only few, possibly ambiguous cues to their geolocation.…
We consider graph classes $\mathcal G$ in which every graph has components in a class $\mathcal{C}$ of connected graphs. We provide a framework for the asymptotic study of $\lvert\mathcal{G}_{n,N}\rvert$, the number of graphs in…
Federated learning over graph-structured data exposes a fundamental mismatch between standard aggregation mechanisms and the operator nature of graph neural networks (GNNs). While federated optimization treats model parameters as elements…
In this work, we study the problem of partitioning a set of graphs into different groups such that the graphs in the same group are similar while the graphs in different groups are dissimilar. This problem was rarely studied previously,…
In this paper, we study the problem of partitioning a graph into connected and colored components called blocks. Using bivariate generating functions and combinatorial techniques, we determine the expected number of blocks when the vertices…
For a given graph $H$, its subdivisions carry the same topological structure. The existence of $H$-subdivisions within a graph $G$ has deep connections with topological, structural and extremal properties of $G$. One prominent example of…
Integer partitions are deeply related to many phenomena in statistical physics. A question naturally arises which is of interest to physics both on "purely" theoretical and on practical, computational grounds. Is it possible to apprehend…
The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…
A geometric graph is a graph drawn in the plane so that its vertices and edges are represented by points in general position and straight line segments, respectively. A vertex of a geometric graph is called pointed if it lies outside of the…
We study the problem of discrete geometric packing. Here, given weighted regions (say in the plane) and points (with capacities), one has to pick a maximum weight subset of the regions such that no point is covered more than its capacity.…
Let G be a graph. The (unlabeled) configuration space of n points on G is the space of all n-element subsets of G. The fundamental group of such a configuration space is called a graph braid group. We use a version of discrete Morse theory…