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Related papers: On the graph isomorphism problem

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We formulate the notion of an isomorphism of GKM graphs. We then show that two GKM graphs have isomorphic graph equivariant cohomology algebras if and only if the graphs are isomorphic.

Algebraic Topology · Mathematics 2019-12-30 Matthias Franz , Hitoshi Yamanaka

The criteria for determining graph isomorphism are crucial for solving graph isomorphism problems. The necessary condition is that two isomorphic graphs possess invariants, but their function can only be used to filtrate and subdivide…

Graphics · Computer Science 2025-08-19 Chuanfu Hu , Aimin Hou

We show that the problem to decide whether two (convex) polytopes, given by their vertex-facet incidences, are combinatorially isomorphic is graph isomorphism complete, even for simple or simplicial polytopes. On the other hand, we give a…

Combinatorics · Mathematics 2007-05-23 Volker Kaibel , Alexander Schwartz

For every integer $g$, isomorphism of graphs of Euler genus at most $g$ can be decided in linear time. This improves previously known algorithms whose time complexity is $n^{O(g)}$ (shown in early 1980's), and in fact, this is the first…

Data Structures and Algorithms · Computer Science 2015-11-10 Ken-ichi Kawarabayashi

In this paper, we introduce the solvabilizer and the solvable graph for a Lie superalgebra and establish their basic properties. Then we define a category which links Lie superalgebras to their solvable substructures. Afterwards, we prove…

Rings and Algebras · Mathematics 2026-02-27 Baojin Zhang , Liming Tang

The isomorphism problem is known to be efficiently solvable for interval graphs, while for the larger class of circular-arc graphs its complexity status stays open. We consider the intermediate class of intersection graphs for families of…

Computational Complexity · Computer Science 2017-04-20 Johannes Köbler , Sebastian Kuhnert , Oleg Verbitsky

The isomorphism problem means to decide if two given finite-dimensional simple algebras over the same centre are isomorphic and, if so, to construct an isomorphism between them. A solution to this problem has applications in computational…

Rings and Algebras · Mathematics 2007-05-23 Timo Hanke

We consider heuristic algorithm for solving graph isomorphism problem. The algorithm based on a successive splitting of the eigenvalues of the matrices which are modifications (to positive defined) of graphs' adjacency matrices.…

General Mathematics · Mathematics 2007-05-23 R. T. Faizullin , A. V. Prolubnikov

We study the isomorphic implication problem for Boolean constraints. We show that this is a natural analog of the subgraph isomorphism problem. We prove that, depending on the set of constraints, this problem is in P, NP-complete, or…

Computational Complexity · Computer Science 2007-05-23 Michael Bauland , Edith Hemaspaandra

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…

Discrete Mathematics · Computer Science 2015-03-19 Paul Bonsma

We study free scalar field theory on a graph, which gives rise to a modified version of discrete Green's function on a graph studied in \cite{CY}. We show that this gives rise to a graph invariant, which is closely related to the 2-dim…

Combinatorics · Mathematics 2015-06-18 An Huang , Shing-Tung Yau , Mei-Heng Yueh

The graph isomorphism (GI) problem, which asks whether two graphs are structurally identical, occupies a unique position in computational complexity -- it is neither known to be solvable in polynomial time, nor proven to be NP-complete. We…

Optimization and Control · Mathematics 2026-05-21 Wenjie Xiao , Mathieu Besançon , Patrick Gelß , Deborah Hendrych , Stefan Klus , Sebastian Pokutta

We report on results about a study of algebraic graph invariants, based on computer exploration, and motivated by graph-isomorphism and reconstruction problems.

Combinatorics · Mathematics 2008-12-17 Pouzet Maurice , Nicolas M. Thiéry

Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…

Combinatorics · Mathematics 2024-08-01 Sergey Kurapov , Maxim Davidovsky

The Graph Isomorphism problem has both theoretical and practical interest. In this paper we present an algorithm, called conauto-1.2, that efficiently tests whether two graphs are isomorphic, and finds an isomorphism if they are. This…

Data Structures and Algorithms · Computer Science 2011-06-23 Jose Luis Lopez-Presa , Antonio Fernandez Anta

We consider complete graphs with edge weights and/or node weights taking values in some set. In the first part of this paper, we show that a large number of graphs are completely determined, up to isomorphism, by the distribution of their…

Combinatorics · Mathematics 2007-10-11 Mireille Boutin , Gregor Kemper

We strengthen and put in a broader perspective previous results of the first two authors on colliding permutations. The key to the present approach is a new non-asymptotic invariant for graphs.

Combinatorics · Mathematics 2007-09-28 János Körner , Claudia Malvenuto , Gábor Simonyi

We study the complexity of the Graph Isomorphism problem on graph classes that are characterized by a finite number of forbidden induced subgraphs, focusing mostly on the case of two forbidden subgraphs. We show hardness results and develop…

Data Structures and Algorithms · Computer Science 2015-03-20 Stefan Kratsch , Pascal Schweitzer

We exhibit an analogy between the problem of pushing forward measurable sets under measure preserving maps and linear relaxations in combinatorialoptimization. We show how invariance of hyperfiniteness of graphings under local isomorphism…

Combinatorics · Mathematics 2021-02-17 László Lovász

The graph isomorphism problem looks deceptively simple, but although polynomial-time algorithms exist for certain types of graphs such as planar graphs and graphs with bounded degree or eigenvalue multiplicity, its complexity class is still…

Discrete Mathematics · Computer Science 2025-07-11 Stefan Klus , Patrick Gelß