Computational problems in graph theory | Hamiltonian paths and cycles | NP-complete problems

Hamiltonian path problem

In the mathematical field of graph theory the Hamiltonian path problem and the Hamiltonian cycle problem are problems of determining whether a Hamiltonian path (a path in an undirected or directed graph that visits each vertex exactly once) or a Hamiltonian cycle exists in a given graph (whether directed or undirected). Both problems are NP-complete. The Hamiltonian cycle problem is a special case of the travelling salesman problem, obtained by setting the distance between two cities to one if they are adjacent and two otherwise, and verifying that the total distance travelled is equal to n (if so, the route is a Hamiltonian circuit; if there is no Hamiltonian circuit then the shortest route will be longer). (Wikipedia).

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Introduction to Hamilton Paths and Hamilton Circuits

This video introduces Hamilton paths and Hamilton circuits. mathispower4u.com

From playlist Graph Theory (Discrete Math)

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Graph Theory: 27. Hamiltonian Graphs and Problem Set

I define a Hamilton path and a Hamilton cycle in a graph and discuss some of their basic properties. Then I pose three questions for the interested viewer. Solutions are in the next video. An introduction to Graph Theory by Dr. Sarada Herke. Related Videos: http://youtu.be/3xeYcRYccro -

From playlist Graph Theory part-5

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Hamiltonian Cycles, Graphs, and Paths | Hamilton Cycles, Graph Theory

What are Hamiltonian cycles, graphs, and paths? Also sometimes called Hamilton cycles, Hamilton graphs, and Hamilton paths, we’ll be going over all of these topics in today’s video graph theory lesson! A Hamilton cycle in a graph G is a cycle containing all vertices of G. A Hamilton path

From playlist Graph Theory

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Graph Theory: 28. Hamiltonian Graph Problems

Here I give solutions to these three problems posed in the previous video: 1. Show that the complete bipartite graph with partite sets of size n and m is Hamiltonian if and only if n and m are equal and greater than or equal to 2. 2. Find a connected graph that has no Hamilton path. 3. Can

From playlist Graph Theory part-6

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A09 The Hamiltonian

Moving on from Lagrange's equation, I show you how to derive Hamilton's equation.

From playlist Physics ONE

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Hamilton Path Application: Home Tour Visiting Each Room Once

This video provides an application involving an Hamilton path. mathispower4u.com

From playlist Graph Theory (Discrete Math)

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Graph Theory: Hamiltonian Circuits and Paths

This lesson explains Hamiltonian circuits and paths. Site: http://mathispower4u.com

From playlist Graph Theory

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5b Hamilton Paths & Circuits

5b Hamilton Paths & Circuits

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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14. P and NP, SAT, Poly-Time Reducibility

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. Defined NTIME(t(n)) complexity classes

From playlist MIT 18.404J Theory of Computation, Fall 2020

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CMU Discrete Mathematics 4/7

Due to the COVID-19 pandemic, Carnegie Mellon University is protecting the health and safety of its community by holding all large classes online. People from outside Carnegie Mellon University are welcome to tune in to see how the class is taught, but unfortunately Prof. Loh will not be o

From playlist CMU 21-228 Discrete Mathematics

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Learning Optimal Control with Stochastic Models of Hamiltonian Dynamics for Shape & Function Optim.

Speaker: Chandrajit Bajaj (7/25/22) Abstract: Shape and Function Optimization can be achieved through Optimal Control over infinite-dimensional search space. All optimal control problems can be solved by first applying the Pontryagin maximum principle, and then computing a solution to the

From playlist Applied Geometry for Data Sciences 2022

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AQC 2016 - Coupled Quantum Fluctuations and Quantum Annealing

A Google TechTalk, June 29, 2016, presented by Layla Hormozi (MIT) ABSTRACT: We study the relative effectiveness of stoquastic and non-stoquastic Hamiltonians consisting of coupled quantum fluctuations compared to Hamiltonians with single spin flips in the performance of quantum annealing.

From playlist Adiabatic Quantum Computing Conference 2016

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Sven Bachmann: A classification of gapped Hamiltonians in d=1

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist SPECIAL 7th European congress of Mathematics Berlin 2016.

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離散数学入門#7: ハミルトングラフと巡回セールスマン問題

早稲田大学の全学部の3〜4年生を対象とする全学オープン科目「離散数学入門」(担当教員:早水 桃子)の授業動画です.文理を問わず,誰でもグラフ理論やグラフアルゴリズムの初歩を学ぶことができます.グラフ理論の定理やグラフに関するアルゴリズムを正しく理解して,現実の諸問題を解決するための応用力を身につけましょう. --------------------------------------------------------------------------------------- 前回は「辺に対する周遊性」ということで,オイラーグラフと郵便配達員問題の話をしましたが,今回は

From playlist 離散数学入門Ⅲ

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Hamiltonian Mechanics in 10 Minutes

In this video I go over the basics of Hamiltonian mechanics. It is the first video of an upcoming series on a full semester university level Hamiltonian mechanics series. Corrections -4:33 the lagrangian should have a minus sign between the first two terms, not a plus.

From playlist Summer of Math Exposition 2 videos

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Edge contraction | Monte Carlo algorithm | K-vertex-connected graph | Graph (discrete mathematics) | Karp's 21 NP-complete problems | PPA (complexity) | Travelling salesman problem | Planar graph | Decision problem | Hamiltonian path | Handshaking lemma | Universal vertex | Big O notation | Regular graph | Dynamic programming | Barnette's conjecture | Degree (graph theory) | Graph theory | DNA computing | Bipartite graph | Mathematics | Complete graph | Inclusion–exclusion principle | SAT solver | FNP (complexity) | Lattice graph | Directed graph | W. T. Tutte | Complexity class