Hamiltonian paths and cycles | NP-complete problems

Hamiltonian completion

The Hamiltonian completion problem is to find the minimal number of edges to add to a graph to make it Hamiltonian. The problem is clearly NP-hard in general case (since its solution gives an answer to the NP-complete problem of determining whether a given graph has a Hamiltonian cycle). The associated decision problem of determining whether K edges can be added to a given graph to produce a Hamiltonian graph is NP-complete. Moreover, Hamiltonian completion belongs to the APX complexity class, i.e., it is unlikely that efficient constant ratio approximation algorithms exist for this problem. The problem may be solved in polynomial time for certain classes of graphs, including series–parallel graphs and their generalizations, which include outerplanar graphs, as well as for a line graph of a treeor a cactus graph. Gamarnik et al. use a linear time algorithm for solving the problem on trees to study the asymptotic number of edges that must be added for sparse random graphs to make them Hamiltonian. (Wikipedia).

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A09 The Hamiltonian

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From playlist Physics ONE

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Hamiltonian Mechanics in 10 Minutes

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From playlist Summer of Math Exposition 2 videos

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The spherical pendulum in the Hamiltonian formalism

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From playlist Programming

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Physics 69 Hamiltonian Mechanics (1 of 18) What is Hamiltonian Mechanics?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is Hamiltonian mechanics, how are the equations derived, how the Hamiltonian equations will simplified into classical mechanics equations. To donate: http://www.ilectureonline.com/donate

From playlist PHYSICS 69 ADVANCED MECHANICS: HAMILTONIAN MECHANICS

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Hamiltonian Simulation and Universal Quantum (...) - T. Cubitt - Main Conference - CEB T3 2017

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

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

From playlist Graph Theory (Discrete Math)

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From playlist Classical Mechanics

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From playlist Graph Theory part-5

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This video is about Hamiltonian graphs and some of their basic properties.

From playlist Basics: Graph Theory

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A Proof on Hamiltonian Complete Bipartite Graphs | Graph Theory, Hamiltonian Graphs

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From playlist Graph Theory

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From playlist Graph Theory

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

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From playlist CSE373 - Analysis of Algorithms - 1997 SBU

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From playlist Mathematics

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From playlist 2017 - T2 - Stochastic Dynamics out of Equilibrium - CEB Trimester

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Non-Equilibrium Steady States of Quantum Non-Hermitian Lattice Models by Aashish Clerk

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From playlist Non-Hermitian Physics (ONLINE)

Related pages

Random graph | Graph (discrete mathematics) | APX | Line graph | Outerplanar graph | Series–parallel graph | Decision problem | Cactus graph | Complexity class