Computational problems in graph theory | Morphisms | Unsolved problems in computer science | Computational complexity theory | Graph algorithms
Unsolved problem in computer science: Can the graph isomorphism problem be solved in polynomial time? (more unsolved problems in computer science) The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic. The problem is not known to be solvable in polynomial time nor to be NP-complete, and therefore may be in the computational complexity class NP-intermediate. It is known that the graph isomorphism problem is in the low hierarchy of class NP, which implies that it is not NP-complete unless the polynomial time hierarchy collapses to its second level. At the same time, isomorphism for many special classes of graphs can be solved in polynomial time, and in practice graph isomorphism can often be solved efficiently. This problem is a special case of the subgraph isomorphism problem, which asks whether a given graph G contains a subgraph that is isomorphic to another given graph H; this problem is known to be NP-complete. It is also known to be a special case of the non-abelian hidden subgroup problem over the symmetric group. In the area of image recognition it is known as the exact graph matching. (Wikipedia).
Graph Theory FAQs: 04. Isomorphism vs Homomorphism
In this video we recall the definition of a graph isomorphism and then give the definition of a graph homomorphism. Then we look at two examples of graph homomorphisms and discuss a special case that relates to graph colourings. -- Graph Theory FAQs by Dr. Sarada Herke. Related videos:
From playlist Graph Theory FAQs
This video defines and gives and example of isomorphic graphs. mathispower4u.com
From playlist Graph Theory (Discrete Math)
Graph Theory: 09. Graph Isomorphisms
In this video I provide the definition of what it means for two graphs to be isomorphic. I illustrate this with two isomorphic graphs by giving an isomorphism between them, and conclude by discussing what it means for a mapping to be a bijection. An introduction to Graph Theory by Dr. Sar
From playlist Graph Theory part-2
4a Isomorphism of Graphs (brief)
From playlist Graph Theory
Graph Theory FAQs: 02. Graph Automorphisms
An automorphism of a graph G is an isomorphism between G and itself. The set of automorphisms of a graph forms a group under the operation of composition and is denoted Aut(G). The automorphisms of a graph describe the symmetries of the graph. We look at a few examples of graphs and det
From playlist Graph Theory FAQs
Graph Theory: Isomorphisms and Connectedness
This video is about isomorphisms between graphs and connectedness of graphs.
From playlist Basics: Graph Theory
Graph Theory: 10. Isomorphic and Non-Isomorphic Graphs
Here I provide two examples of determining when two graphs are isomorphic. If they are isomorphic, I give an isomorphism; if they are not, I describe a property that I show occurs in only one of the two graphs. Here is a related video in which I show how to check for whether these examp
From playlist Graph Theory part-2
What are Isomorphic Graphs? | Graph Isomorphism, Graph Theory
How do we formally describe two graphs "having the same structure"? The term for this is "isomorphic". Two graphs that have the same structure are called isomorphic, and we'll define exactly what that means with examples in today's video graph theory lesson! Check out the full Graph Theor
From playlist Graph Theory
Graph Theory: 14b. Basic Graph Theory Problem Set 2
--An introduction to Graph Theory by Dr. Sarada Herke.
From playlist Graph Theory part-3
Global symmetry from local information: The Graph Isomorphism Problem – László Babai – ICM2018
Combinatorics | Mathematical Aspects of Computer Science Invited Lecture 13.4 | 14.5 Global symmetry from local information: The Graph Isomorphism Problem László Babai Abstract: Graph Isomorphism (GI) is one of a small number of natural algorithmic problems with unsettled complexity stat
From playlist Combinatorics
25. Interactive Proof Systems, IP
MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY Quickly reviewed last lecture. Introduced the interactive proof syste
From playlist MIT 18.404J Theory of Computation, Fall 2020
Lower bounds for subgraph isomorphism – Benjamin Rossman – ICM2018
Mathematical Aspects of Computer Science Invited Lecture 14.3 Lower bounds for subgraph isomorphism Benjamin Rossman Abstract: We consider the problem of determining whether an Erdős–Rényi random graph contains a subgraph isomorphic to a fixed pattern, such as a clique or cycle of consta
From playlist Mathematical Aspects of Computer Science
MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015
Lecture 23 - Cook's Theorem & Harder Reductions
This is Lecture 23 of the CSE373 (Analysis of Algorithms) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1997. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/video-lectures/1997/lecture25.pdf
From playlist CSE373 - Analysis of Algorithms - 1997 SBU
Soledad Villar: "Graph neural networks for combinatorial optimization problems"
Machine Learning for Physics and the Physics of Learning 2019 Workshop IV: Using Physical Insights for Machine Learning "Graph neural networks for combinatorial optimization problems" Soledad Villar - New York University Abstract: Graph neural networks are natural objects to express fu
From playlist Machine Learning for Physics and the Physics of Learning 2019
MATH1081 Discrete Maths: Chapter 5 Question 15 a, c
MATH1081 Discrete Mathematics This problem is about graph isomorphism. We exhibit an explicit isomorphism between two isomorphic graphs in a), and show why an isomorphism doesn't exist in c). Presented by Thomas Britz, School of Mathematics and Statistics, Faculty of Science, UNSW Austra
From playlist MATH1081 Discrete Mathematics
"Symmetrie und Ähnlichkeit" - Vortrag von Prof. Martin Grohe
Aufzeichnung des Vortrags "Symmetrie und Ähnlichkeit" von Prof. Dr. Martin Grohe (RWTH Aachen) im Rahmen der öffentlichen Reihe "Brücken in der Mathematik" an der WWU Münster. Darum geht es: Muster auf Schmetterlingsflügeln, Schneekristalle, Blütenblätter – symmetrische Strukturen sind in
From playlist Brücken in der Mathematik