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Longest path problem

In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph. A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges. In…

Science, Special classes of graphs & Parameterized complexity

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Overview

NP-hardness

Acyclic graphs

Approximation

Parameterized complexity

Special classes of graphs

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Longest path problem

Nodes59
Edges58
Triples25
Avg. degree1.97
Density0.033898
Components1

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Longest path problem

Top relations

related to NP-hardness · 9
Longest path problem → Because, Hamiltonian, If, In, NP-complete, NP-hard, The, The NP-hardness, Therefore
related to Approximation · 8
Longest path problem → Björklund, For, Husfeldt, In, Khanna, NP, Omega, The
related to Parameterized complexity · 6
Longest path problem → Apply, For, Let, Perform, The, Use
is a · 2
Longest path problem → problem of finding a simple path of maximum length in a given graph, same as the Travelling salesman path problem

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Important terminology

path longest graphs problem length time graph displaystyle also algorithm polynomial vertices number simple paths acyclic known directed given solved

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Longest path problemis aproblem of finding a simple path of maximum length in a given graph0.90text
Longest path problemis asame as the Travelling salesman path problem0.90text
Longest path problemrelated to ApproximationBjörklund0.60section
Longest path problemrelated to ApproximationHusfeldt0.60section
Longest path problemrelated to ApproximationKhanna0.60section
Longest path problemrelated to ApproximationThe0.60section
Longest path problemrelated to ApproximationOmega0.60section
Longest path problemrelated to ApproximationFor0.60section
Longest path problemrelated to ApproximationNP0.60section
Longest path problemrelated to ApproximationIn0.60section
Longest path problemrelated to NP-hardnessThe NP-hardness0.60section
Longest path problemrelated to NP-hardnessHamiltonian0.60section

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