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As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to…
$ $We study the $d$-Uniform Hypergraph Matching ($d$-UHM) problem: given an $n$-vertex hypergraph $G$ where every hyperedge is of size $d$, find a maximum cardinality set of disjoint hyperedges. For $d\geq3$, the problem of finding the…
In this paper we investigate the extremal relationship between two well-studied graph parameters: the order of the largest homogeneous set in a graph $G$ and the maximal number of distinct degrees appearing in an induced subgraph of $G$,…
The paper considers the NP-hard graph vertex coloring problem, which differs from traditional problems in which it is required to color vertices with a given (or minimal) number of colors so that adjacent vertices have different colors. In…
We consider the algorithmic decision problem that takes as input an $n$-vertex $k$-uniform hypergraph $H$ with minimum codegree at least $m-c$ and decides whether it has a matching of size $m$. We show that this decision problem is fixed…
In this paper we consider a variation of a recoloring problem, called the Color-Fixing. Let us have some non-proper $r$-coloring $\varphi$ of a graph $G$. We investigate the problem of finding a proper $r$-coloring of $G$, which is "the…
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
This paper builds theoretical foundations for the recovery of a newly proposed class of smooth graph signals, approximately bandlimited graph signals, under three sampling strategies: uniform sampling, experimentally designed sampling and…
We derive new results for the performance of a simple greedy algorithm for finding large independent sets and matchings in constant degree regular graphs. We show that for $r$-regular graphs with $n$ nodes and girth at least $g$, the…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…
We study the fundamental limits for reconstruction in weighted graph (or matrix) database alignment. We consider a model of two graphs where $\pi^*$ is a planted uniform permutation and all pairs of edge weights $(A_{i,j},…
In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…
Partial graph matching extends traditional graph matching by allowing some nodes to remain unmatched, enabling applications in more complex scenarios. However, this flexibility introduces additional complexity, as both the subset of nodes…
Temporal graphs are graphs where the topology and/or other properties of the graph change with time. They have been used to model applications with temporal information in various domains. Problems on static graphs become more challenging…
The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to…
We study the graph alignment problem over two independent Erd\H{o}s-R\'enyi graphs on $n$ vertices, with edge density $p$ falling into two regimes separated by the critical window around $p_c=\sqrt{\log n/n}$. Our result reveals an…
Graph matching is one of the most significant graph analytic tasks, which aims to find the node correspondence across different graphs. Most existing graph matching approaches mainly rely on topological information, whose performances are…
In this paper, we propose a family of label recovery problems on weighted Euclidean random graphs. The vertices of a graph are embedded in $\mathbb{R}^d$ according to a Poisson point process, and are assigned to a discrete community label.…
We consider constrained variants of graph homomorphisms such as embeddings, monomorphisms, full homomorphisms, surjective homomorpshims, and locally constrained homomorphisms. We also introduce a new variation on this theme which derives…