Related papers: Dynamic approach to k-forcing
A dynamical system is called contractive if any two solutions approach one another at an exponential rate. More precisely, the dynamics contracts lines at an exponential rate. This property implies highly ordered asymptotic behavior…
In this paper, we introduce a new concept namely degree polynomial for vertices of a simple graph. This notion leads to a concept namely degree polynomial sequence which is stronger than the concept of degree sequence. After obtaining the…
In this work, we present a methodology for devising forward-backward methods for finding zeros in the sum of a finite number of maximally monotone operators. We extend the framework and techniques from [SIAM J. Optim., 34 (2024), pp.…
Given query access to an undirected graph $G$, we consider the problem of computing a $(1\pm\epsilon)$-approximation of the number of $k$-cliques in $G$. The standard query model for general graphs allows for degree queries, neighbor…
We consider the optimisation problem of adding $k$ links to a given network, such that the resulting effective graph resistance is as small as possible. The problem was recently proven to be NP-hard, such that optimal solutions obtained…
We define a new notion of compressibility of a set of numbers through the dynamics of a polynomial function. We provide approaches to solve the problem by reducing it to the multi-criteria traveling salesman problem through a series of…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
We show that the number of $k$-matching in a given undirected graph $G$ is equal to the number of perfect matching of the corresponding graph $G_k$ on an even number of vertices divided by a suitable factor. If $G$ is bipartite then one can…
In this work, which was inspired by the article [2] by M. V. Velasco and A. R. Villena, we obtain a characterization for probably continuous operators and show that the probability of a linear random operator being continuous coincides with…
This paper introduces a novel framework for graph sparsification that preserves the essential learning attributes of original graphs, improving computational efficiency and reducing complexity in learning algorithms. We refer to these…
We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the…
We consider the problem of tensor completion with graphs serving as side information to represent interrelationships among variables. Existing approaches suffer from several limitations: (1) they are often task-specific and lack generality…
We consider two graph optimization problems called vector domination and total vector domination. In vector domination one seeks a small subset S of vertices of a graph such that any vertex outside S has a prescribed number of neighbors in…
Closeness is an important measure of network centrality. In this article we will calculate the closeness of graphs, created by using operations on graphs. We will prove a formula for the closeness of shadow graphs. We will calculate the…
This thesis studies the graph alignment problem, the noisy version of the graph isomorphism problem, which aims to find a matching between the nodes of two graphs which preserves most of the edges. Focusing on the planted version where the…
There is an extensive literature on dynamic algorithms for a large number of graph theoretic problems, particularly for all varieties of shortest path problems. Germane to this paper are a number fully dynamic algorithms that are known for…
Let $G$ be a simple and finite graph without isolated vertices. In this paper we study forcing sets (zero forcing sets) which induce a subgraph of $G$ without isolated vertices. Such a set is called a total forcing set, introduced and first…
We enumerate factorisations of the complete graph into spanning regular graphs in several cases, including when the degrees of all the factors except for one or two are small. The resulting asymptotic behaviour is seen to generalise the…
A graph $G$ is a {\em chordal-$k$-generalized split graph} if $G$ is chordal and there is a clique $Q$ in $G$ such that every connected component in $G[V \setminus Q]$ has at most $k$ vertices. Thus, chordal-$1$-generalized split graphs are…
One of the simplest ways to decide whether a given finite sequence of positive integers can arise as the degree sequence of a simple graph is the greedy algorithm of Havel and Hakimi. This note extends their approach to directed graphs. It…