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A conjecture on cycle-pancyclism in tournaments

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Galeana-Sánchez H., Rajsbaum S.

Discussiones Mathematicae Graph Theory

1998

tom 18

nr 2

243-251

Let T be a hamiltonian tournament with n vertices and γ a hamiltonian cycle of T. In previous works we introduced and studied the concept of cycle-pancyclism to capture the following question: What is the maximum intersection with γ of a cycle of length k? More precisely, for a cycle Cₖ of length k in T we denote $I_γ (Cₖ) = |A(γ)∩A(Cₖ)|$, the number of arcs that γ and Cₖ have in common. Let $f(k,T,γ) = max{I_γ(Cₖ)|Cₖ ⊂ T}$ and f(n,k) = min{f(k,T,γ)|T is a hamiltonian tournament with n vertices, and γ a hamiltonian cycle of T}. In previous papers we gave a characterization of f(n,k). In particular, the characterization implies that f(n,k) ≥ k-4. The purpose of this paper is to give some support to the following original conjecture: for any vertex v there exists a cycle of length k containing v with f(n,k) arcs in common with γ.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Galeana-Sánchez H.

1 Rajsbaum S.

1 1998

Wyniki wyszukiwania

A conjecture on cycle-pancyclism in tournaments