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Algorithms for long paths in graphs. (English) Zbl 1117.68057
Summary: 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 a 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.

##### MSC:
 68R10 Graph theory (including graph drawing) in computer science 05C85 Graph algorithms (graph-theoretic aspects) 05C38 Paths and cycles
##### Keywords:
Hamiltonian; long path; neighborhood condition
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##### References:
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