Related papers: Graph equivalence and characterization via a conti…

Graph isomorphism problem is a known hard problem. In this paper, a novel randomized algorithm is proposed for this problem which is very simple and fast. It solves the graph isomorphism problem with running time O(n^2.373) for any pair of…

Graph comparison is fundamentally important for many applications such as the analysis of social networks and biological data and has been a significant research area in the pattern recognition and pattern analysis domains. Nowadays, the…

We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…

We characterise the form of all simple, finite graphs for which the girth of the graph is equal to the circumference of the graph. We apply this to prove a bound on the number of edges in such a graph.

We consider the problem of finding a subgraph of a given graph minimizing the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already for bipartite graphs when the functions are convex on…

The graph isomorphism problem is a main problem which has numerous applications in different fields. Thus, finding an efficient and easy to implement method to discriminate non-isomorphic graphs is valuable. In this paper, a new method is…

The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…

Graphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods,…

We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…

As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…

We focus on evolution equations on co-evolving, infinite, graphs and establish a rigorous link with a class of nonlinear continuity equations, whose vector fields depend on the graphs considered. More precisely, weak solutions of the…

Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and…

An approach to the equivalence problem of vector valued maps is offered which, in particular, covers the equivalence problem of paths and patches of differential geometry with respect to different motion groups. In the last case, in…

Current graph neural networks (GNNs) lack generalizability with respect to scales (graph sizes, graph diameters, edge weights, etc..) when solving many graph analysis problems. Taking the perspective of synthesizing graph theory programs,…

It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties…

We raise some questions about graph polynomials, highlighting concepts and phenomena that may merit consideration in the development of a general theory. Our questions are mainly of three types: When do graph polynomials have reduction…

This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…

We discuss the problem of extending data mining approaches to cases in which data points arise in the form of individual graphs. Being able to find the intrinsic low-dimensionality in ensembles of graphs can be useful in a variety of…

In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…

We consider apictorial edge-matching puzzles, in which the goal is to arrange a collection of puzzle pieces with colored edges so that the colors match along the edges of adjacent pieces. We devise an algebraic representation for this…