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On the number of Hamiltonian cycles in tournaments

✍ Scribed by Carsten Thomassen

Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
949 KB
Volume
31
Category
Article
ISSN
0012-365X

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✦ Synopsis

The main results assert that the minimum number of Hamiltonian bypasses in a strong tournament of order n and the minimum number of Hamiltonian cycles in a 2-connected tournament of order n increase exponentially with n. Furthermore, the number of Hamiltonian cycles in a tournament increases at least exponentially with the minimum outdegree of the tournament. Finally, for each k a 1 there are infinitely many tournaments with precisely k Hamiltonian cycles.

πŸ“œ SIMILAR VOLUMES

Hamiltonian tournaments with the least n
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## Abstract We characterize the family of hamiltonian tournaments with the least number of 3‐cycles, studying their structure and their score sequence. Furthermore, we obtain the number of nonisomorphic tournaments of this family.

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