Solution of a conjecture of Tewes and Volkmann regarding extendable cycles in in-tournaments

A directed cycle C of a digraph D is extendable if there exists a directed cycle C′ in D that contains all vertices of C and an additional one. In 1989, Hendry defined a digraph D to be cycle extendable if it contains a directed cycle and every non‐Hamiltonian directed cycle of D is extendable. Furt...

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Bibliographic Details
Published in:Journal of graph theory 2010-01, Vol.63 (1), p.82-92
Main Author: Meierling, Dirk
Format: Article
Language:English
Subjects:
extendable cycles
in-tournaments
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Summary:A directed cycle C of a digraph D is extendable if there exists a directed cycle C′ in D that contains all vertices of C and an additional one. In 1989, Hendry defined a digraph D to be cycle extendable if it contains a directed cycle and every non‐Hamiltonian directed cycle of D is extendable. Furthermore, D is fully cycle extendable if it is cycle extendable and every vertex of D belongs to a directed cycle of length three. In 2001, Tewes and Volkmann extended these definitions in considering only directed cycles whose length exceed a certain bound 3≤k
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.20408