Algorithms for long paths in graphs

Authors:
Zhao Zhang;Hao Li
Affiliations:
College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, China;Laboratoire de Recherche en Informatique, UMR 8623, C.N.R.S.-Université de Paris-sud, 91405-Orsay cedex, France and School of Mathematics and Statistics, Lanzhou University, 730000 Lanzhou, G ...
Venue:
Theoretical Computer Science
Year:
2007

Citing 10
Cited 4

Hamiltonism, degree sum and neighborhood intersections

Discrete Mathematics
On linear time minor tests with depth-first search

Journal of Algorithms
Color-coding: a new method for finding simple paths, cycles and other small subgraphs within large graphs

STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Longest cycles in 3-connected graphs

Discrete Mathematics
Finding long paths and cycles in sparse Hamiltonian graphs

STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
An approximation algorithm for finding a long path in Hamiltonian graphs

SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On the Approximation of Finding A(nother) Hamilton Cycle in Cubic Hamilton Graphs (Extended Abstract)

STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Finding a Path of Superlogarithmic Length

SIAM Journal on Computing
Graph Theory With Applications

Graph Theory With Applications
Combinatorial Optimization: Theory and Algorithms

Combinatorial Optimization: Theory and Algorithms

Algorithm for two disjoint long paths in 2-connected graphs

Theoretical Computer Science
The longest path problem is polynomial on cocomparability graphs

WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
A linear-time algorithm for the longest path problem in rectangular grid graphs

Discrete Applied Mathematics
An efficient parallel algorithm for the longest path problem in meshes

The Journal of Supercomputing

Quantified Score

Hi-index	5.23

Visualization

Abstract

We obtain a polynomial algorithm in O(nm) time to find a long path in any graph with n vertices and m edges. The length of the path is bounded by a parameter defined on neighborhood condition of any three independent vertices of the path. An example is given to show that this bound is better than several classic results.