Related papers: A proof of Pieri's formula using the generalized S…
We give a new approach to handling hypergraph regularity. This approach allows for vertex-by-vertex embedding into regular partitions of hypergraphs, and generalises to regular partitions of sparse hypergraphs. We also prove a corresponding…
Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing…
In this paper, we extend a lower bound estimate for Steklov eigenvalues by Perrin \cite{Pe} on unit-weighted graphs to general weighted graphs and characterise its rigidity.
We identify all $[1, \lambda, 8]$-cycle regular $I$-graphs and all $[1, \lambda, 8]$-cycle regular double generalized Petersen graphs. As a consequence we describe linear recognition algorithms for these graph families. Using structural…
We show that if $n=7k/i$ with $i \in \{1,2,3\}$ then the cop number of the generalised Petersen graph $GP(n,k)$ is $4$, with some small previously-known exceptions. It was previously proved by Ball et al. (2015) that the cop number of any…
This paper introduces a Bayesian framework for image inversion by deriving a probabilistic counterpart to the regularization-by-denoising (RED) paradigm. It additionally implements a Monte Carlo algorithm specifically tailored for sampling…
The generalized coloring numbers of Kierstead and Yang (Order 2003) offer an algorithmically-useful characterization of graph classes with bounded expansion. In this work, we consider the hardness and approximability of these parameters.…
General factors are a generalization of matchings. Given a graph $G$ with a set $\pi(v)$ of feasible degrees, called a degree constraint, for each vertex $v$ of $G$, the general factor problem is to find a (spanning) subgraph $F$ of $G$…
Probabilistic graphical models provide a powerful tool to describe complex statistical structure, with many real-world applications in science and engineering from controlling robotic arms to understanding neuronal computations. A major…
We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.
In this paper we consider the generalized Reeder's puzzle, introduced by Reeder in 2005 and generalized by Borovoi and Evenor in 2016. We give a detailed solution of the puzzle for the graphs of Dynkin diagrams and affine Dynkin diagrams.…
In this paper we obtain closed formulae for several parameters of generalized Sierpi\'{n}ski graphs $S(G,t)$ in terms of parameters of the base graph $G$. In particular, we focus on the chromatic, vertex cover, clique and domination…
We use known characterizations of generalized Paley graphs which are cartesian decomposable to explicitly compute the spectra of the corresponding associated irreducible cyclic codes. As applications, we give reduction formulas for the…
A graph $G=(V,E)$ is called $d$-rigid if, for a generic embedding of its vertices in $\mathbb{R}^d$, every edge-length preserving continuous motion of the vertices preserves the distances between all pairs of non-adjacent vertices as well.…
Petrie symmetric functions $G(k,n)$, also known as truncated homogeneous symmetric functions or modular complete symmetric functions, form a class of symmetric functions interpolating between the elementary symmetric functions $e_n$ and the…
We extend the Penrose polynomial, originally defined only for plane graphs, to graphs embedded in arbitrary surfaces. Considering this Penrose polynomial of embedded graphs leads to new identities and relations for the Penrose polynomial…
We prove that there is an algorithm to determine if a given finite graph is an induced subgraph of a given curve graph.
Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features…
We introduce a new distributed algorithm for aligning graphs or finding substructures within a given graph. It is based on the cavity method and is used to study the maximum-clique and the graph-alignment problems in random graphs. The…
Baker devised a powerful technique to obtain approximation schemes for various problems restricted to planar graphs. Her technique can be directly extended to various other graph classes, among the most general ones the graphs avoiding a…