Morphisms | Graph theory

Graph homomorphism

In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a function between the vertex sets of two graphs that maps adjacent vertices to adjacent vertices. Homomorphisms generalize various notions of graph colorings and allow the expression of an important class of constraint satisfaction problems, such as certain scheduling or frequency assignment problems.The fact that homomorphisms can be composed leads to rich algebraic structures: a preorder on graphs, a distributive lattice, and a category (one for undirected graphs and one for directed graphs).The computational complexity of finding a homomorphism between given graphs is prohibitive in general, but a lot is known about special cases that are solvable in polynomial time. Boundaries between tractable and intractable cases have been an active area of research. (Wikipedia).

Graph homomorphism
Video thumbnail

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

Video thumbnail

Homomorphisms in abstract algebra

In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu

From playlist Abstract algebra

Video thumbnail

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

Video thumbnail

Isomorphic Graphs

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

From playlist Graph Theory (Discrete Math)

Video thumbnail

Homomorphisms in abstract algebra examples

Yesterday we took a look at the definition of a homomorphism. In today's lecture I want to show you a couple of example of homomorphisms. One example gives us a group, but I take the time to prove that it is a group just to remind ourselves of the properties of a group. In this video th

From playlist Abstract algebra

Video thumbnail

Group Homomorphisms - Abstract Algebra

A group homomorphism is a function between two groups that identifies similarities between them. This essential tool in abstract algebra lets you find two groups which are identical (but may not appear to be), only similar, or completely different from one another. Homomorphisms will be

From playlist Abstract Algebra

Video thumbnail

What is a Group Homomorphism? Definition and Example (Abstract Algebra)

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys What is a Group Homomorphism? Definition and Example (Abstract Algebra)

From playlist Abstract Algebra

Video thumbnail

14. Graph limits I: introduction

MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Graph limits provide a beautiful analytic framework for s

From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

Video thumbnail

Graph Density Inequalities, Sums of Squares and Tropicalization - Annie Raymond

Computer Science/Discrete Mathematics Seminar I Topic: Graph Density Inequalities, Sums of Squares and Tropicalization Speaker: Annie Raymond Affiliation: University of Massachusetts Amherst Date: February 01, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Graph Theory: Isomorphisms and Connectedness

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

From playlist Basics: Graph Theory

Video thumbnail

J. Aramayona - MCG and infinite MCG (Part 3)

The first part of the course will be devoted to some of the classical results about mapping class groups of finite-type surfaces. Topics may include: generation by twists, Nielsen-Thurston classification, abelianization, isomorphic rigidity, geometry of combinatorial models. In the secon

From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications

Video thumbnail

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

Video thumbnail

Volodymyr Nekrashevych: Contracting self-similar groups and conformal dimension

HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 20, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM'

From playlist Dynamical Systems and Ordinary Differential Equations

Video thumbnail

Ben Knudsen (7/28/22): The topological complexity of pure graph braid groups is stably maximal

I will discuss a proof of Farber's conjecture on the topological complexity of configuration spaces of graphs. The argument eschews cohomology, relying instead on group theoretic estimates for higher topological complexity due to Farber–Oprea following Grant–Lupton–Oprea.

From playlist Topological Complexity Seminar

Video thumbnail

Stability and sofic approximations for product groups and property (tau) - Adrian Ioana

Stability and Testability Topic: Stability and sofic approximations for product groups and property (tau) Speaker: Adrian Ioana Affiliation: University of California, San Diego Date: November 4, 2020 For more video please visit http://video.ias.edu

From playlist Stability and Testability

Video thumbnail

Danny Calegari: Big Mapping Class Groups - lecture 3

Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-h

From playlist Topology

Video thumbnail

Workshop 1 "Operator Algebras and Quantum Information Theory" - CEB T3 2017 - V.Paulsen

Vern Paulsen (Waterloo) / 12.09.17 Title: C*-algebras and Synchronous Games. Abstract: In recent years a deep connection has been found between Connnes’ embedding problem and Tsirelson’s questions about various sets of probabilistic quantum correlations, called local, quantum, quantum a

From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester

Video thumbnail

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

Related pages

Graph (discrete mathematics) | Gallai–Hasse–Roy–Vitaver theorem | Oriented coloring | Polynomial-time reduction | Complement graph | Distributive lattice | Fractional coloring | Graph theory | Equivalence class | Bipartite graph | Cycle graph | Local search (constraint satisfaction) | Mycielskian | Covering graph | Dense order | Antichain | Inverse function | Primal constraint graph | Hypercube graph | Median graph | Homeomorphism (graph theory) | Exponential object | Product (category theory) | Complexity of constraint satisfaction | Girth (graph theory) | Injective function | Path graph | Exponential time hypothesis | Grötzsch graph | Hedetniemi's conjecture | Complete graph | Category (mathematics) | P versus NP problem | Circular coloring | Connectivity (graph theory) | Join and meet | Glossary of graph theory | Decision problem | Bipartite double cover | Sidorenko's conjecture | Graph rewriting | Constraint satisfaction problem | Computational complexity | Neighbourhood (graph theory) | Homomorphism | Complete bipartite graph | Preorder | NP-intermediate | Mathematics | Surjective function | Backtracking | Graph isomorphism | L(2,1)-coloring | Orientation (graph theory) | Bijection | Time complexity | Kneser graph | Cartesian closed category | Brute-force search | Scheduling (production processes) | Electronic Journal of Combinatorics | Tensor product of graphs | Odd number | Dynamic programming | T-coloring | Graph minor | Induced subgraph | Vertex (graph theory) | Loop (graph theory) | Graph coloring | Initial and terminal objects | Treewidth | Chromatic number | Structure (mathematical logic) | Multiple edges | Heyting algebra | Parameterized complexity