相关论文: A Polynomial Time Algorithm for Graph Isomorphism
A connected graph can be associated with two distinct evolution algebras. In the first case, the structural matrix is the adjacency matrix of the graph itself. In the second case, the structural matrix is the transition probabilities matrix…
We show that if the two parts of a finite bipartite graph have the same degree sequence, then there is a bipartite graph, with the same degree sequences, which is symmetric, in that it has an involutive graph automorphism that interchanges…
A matching $M$ in a graph $G$ is said to be uniquely restricted if there is no other matching in $G$ that matches the same set of vertices as $M$. We describe a polynomial-time algorithm to compute a maximum cardinality uniquely restricted…
We describe polynomial time algorithms for determining whether an undirected graph may be embedded in a distance-preserving way into the hexagonal tiling of the plane, the diamond structure in three dimensions, or analogous structures in…
The group isomorphism problem asks whether two finite groups given by their Cayley tables are isomorphic or not. Although there are polynomial-time algorithms for some specific group classes, the best known algorithm for testing isomorphism…
We show that a nontrivial graph isomorphism problem of two undirected graphs, and more generally, the permutation similarity of two given $n\times n$ matrices, is equivalent to equalities of volumes of the induced three convex bounded…
We describe an algorithm which, given two essential curves on a surface $S$, computes their distance in the curve graph of $S$, up to multiplicative and additive errors. As an application, we present an algorithm to decide the…
We present in this short note a polynomial graph extension procedure that can be used to improve any graph isomorphism algorithm. This construction propagates new constraints from the isomorphism constraints of the input graphs (denoted by…
There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a…
Notions of graph similarity provide alternative perspective on the graph isomorphism problem and vice-versa. In this paper, we consider measures of similarity arising from mismatch norms as studied in Gervens and Grohe: the edit distance…
Networks are often studied using the eigenvalues of their adjacency matrix, a powerful mathematical tool with a wide range of applications. Since in real systems the exact graph structure is not known, researchers resort to random graphs to…
We give a family of counter examples showing that the two sequences of polytopes $\Phi_{n,n}$ and $\Psi_{n,n}$ are different. These polytopes were defined recently by S. Friedland in an attempt at a polynomial time algorithm for graph…
Graphs are widely used to model complicated data semantics in many application domains. In this paper, two novel and efficient algorithms Fast-ON and Fast-P are proposed for solving the subgraph isomorphism problem. The two algorithms are…
The interval graph for a set of intervals on a line consists of one vertex for each interval, and an edge for each intersecting pair of intervals. A probe interval graph is a variant that is motivated by an application to genomics, where…
The traditional adjacency matrix of a mixed graph is not symmetric in general, hence its eigenvalues may be not real. To overcome this obstacle, several authors have recently defined and studied various Hermitian adjacency matrices of…
Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment,…
The Subgraph Isomorphism problem asks, given a host graph G on n vertices and a pattern graph P on k vertices, whether G contains a subgraph isomorphic to P. The restriction of this problem to planar graphs has often been considered. After…
The graph isomorphism is to determine whether two graphs are isomorphic. A closely related problem is automorphism detection, where an isomorphism between two graphs is a bijection between their vertex sets that preserves adjacency, and an…
Two matrices are said to be principal minor equivalent if they have equal corresponding principal minors of all orders. We give a characterization of principal minor equivalence and a deterministic polynomial time algorithm to check if two…
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…