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Vertex heaviest paths and cycles in quasi-transitive digraphs

✍ Scribed by Jørgen Bang-Jensen; Gregory Gutin

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
381 KB
Volume
163
Category
Article
ISSN
0012-365X

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✦ Synopsis

A digraph D is called a quasi-transitive digraph (QTD) if for any triple x,y,z of distinct vertices of D such that (x,y) and (y,z) are arcs of D there is at least one at': from x to z or from z to x. Solving a conjecture by Bangdensen and Huang (1995), Gutin (1995) described polynomial algorithms for finding a Hamiltonian cycle and a Hamiltonian path (if it exists) in a QTD. The approach taken in that paper cannot be used to find a longest path or cycle in polynomial time. We present a principally new approach that leads to polynomial algorithms for iinding vertex heaviest paths and cycles in QTDs with non-negative weights on the vertices. This, in particular, provides an answer to a question by N. Alon on longest paths and cycles in QTDs.

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