Computational problems in graph theory | Graph algorithms | NP-complete problems

Subgraph isomorphism problem

In theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs G and H are given as input, and one must determine whether G contains a subgraph that is isomorphic to H.Subgraph isomorphism is a generalization of both the maximum clique problem and the problem of testing whether a graph contains a Hamiltonian cycle, and is therefore NP-complete. However certain other cases of subgraph isomorphism may be solved in polynomial time. Sometimes the name subgraph matching is also used for the same problem. This name puts emphasis on finding such a subgraph as opposed to the bare decision problem. (Wikipedia).

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Isomorphic Graphs

This video defines and gives and example of isomorphic graphs. mathispower4u.com

From playlist Graph Theory (Discrete Math)

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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

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Isomorphisms in abstract algebra

In this video I take a look at an example of a homomorphism that is both onto and one-to-one, i.e both surjective and injection, which makes it a bijection. Such a homomorphism is termed an isomorphism. Through the example, I review the construction of Cayley's tables for integers mod 4

From playlist Abstract algebra

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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

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What is a Subgraph? | Graph Theory

What is a subgraph? We go over it in today's math lesson! If you're familiar with subsets, then subgraphs are probably exactly what you think they are. Recall that a graph G = (V(G), E(G)) is an ordered pair with a vertex set V(G) and an edge set E(G). Then, another graph H = (V(H), E(H))

From playlist Graph Theory

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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

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Lecture 22 - More Reductions

This is Lecture 22 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/lecture24.pdf

From playlist CSE373 - Analysis of Algorithms - 1997 SBU

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Author Interview - Equivariant Subgraph Aggregation Networks

Paper link: https://arxiv.org/abs/2110.02910 Primary authors: Beatrice Bevilacqua (@beabevi_), Fabrizio Frasca (@ffabffrasca), Derek Lim (@dereklim_lzh) Join my FREE course Basics of Graph Neural Networks (https://www.graphneuralnets.com/p/basics-of-gnns/?src=yt)

From playlist Graph Neural Networks

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AMMI 2022 Course "Geometric Deep Learning" - Seminar 2 (Subgraph GNNs) - Fabrizio Frasca

Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July 2022 Seminar 2 - Subgraphs for more powerful GNNs - Fabrizio Frasca (Twitter) Slides: https://www.dropbox.com/s/tnuhppf1fqmv6y9/AIMS%202020%20-%20Seminar%202%20-%20Subgra

From playlist AMMI Geometric Deep Learning Course - Second Edition (2022)

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Subgraphs

A subgraph consist of nodes and edges of a larger graph. In this tutorial I show you what a subgraph is and present an elegant representation in Mathematica. You can learn more about Mathematica on my Udemy course at https://www.udemy.com/mathematica/ PS! Wait until Udemy has a sale an

From playlist Introducing graph theory

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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

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Graph Theory: Isomorphisms and Connectedness

This video is about isomorphisms between graphs and connectedness of graphs.

From playlist Basics: Graph Theory

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What are Signed Graphs?

This video introduces signed graphs and signed graph theory. Signed graphs are graphs where the edges are given a positive or negative sign. They see applications in scheduling (signed graph coloring specifically), data science, social psychology, and more. In future videos we'll look at c

From playlist Summer of Math Exposition Youtube Videos

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Haggai Maron: Subgraph-based networks for expressive, efficient, and domain-independent graph...

CONFERENCE Recording during the thematic meeting : " Machine Learning and Signal Processing on Graphs" the November 8, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians

From playlist Mathematical Aspects of Computer Science

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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

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Live CEOing Ep 52: Chemistry in the Wolfram Language

Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Chemistry in the Wolfram Language.

From playlist Behind the Scenes in Real-Life Software Design

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Sparse Graph Limits 1: Left and Right convergence - Jennifer Chayes

Conference on Graphs and Analysis Jennifer Chayes June 6, 2012 More videos on http://video.ias.edu

From playlist Mathematics

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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

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Han Huang - When can we recover an Erdos-Renyi graph from its local structure? - IPAM at UCLA

Recorded 09 February 2022. Han Huang of the Georgia Institute of Technology Department of Mathematics presents "When can we recover an Erdos-Renyi graph from its local structure?" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: Suppose we have a graph G. F

From playlist Workshop: Calculus of Variations in Probability and Geometry

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