## On a classification of Hamiltonian tournaments.(English)Zbl 0679.05035

Let T be a tournament. Then cc(T), the cyclic characteristic of T, is the length of the shortest cycle $$C=v_ 1...v_ kv_ 1$$ with the property: for each vertex $$v\in T-C$$ there is at least one arc from v to C and at least one arc from C to v. The main result of the paper is that for each Hamiltonian tournament $$H_ n$$ on n vertices, $$3\leq cc(H_ n)\leq n-2$$, and for each $$n\geq 5$$ and k, $$3\leq k\leq n-2$$, there exists a Hamiltonian tournament with $$cc(H_ n)=k$$.
Reviewer: P.Horak

### MSC:

 05C20 Directed graphs (digraphs), tournaments 05C45 Eulerian and Hamiltonian graphs

### Keywords:

cyclic characteristic; Hamiltonian tournament
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