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Pancyclism and small cycles in graphs

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Faudree R., Favaron O., Flandrin E., Li H.

Discussiones Mathematicae Graph Theory

1996

tom 16

nr 1

27-40

We first show that if a graph G of order n contains a hamiltonian path connecting two nonadjacent vertices u and v such that d(u)+d(v) ≥ n, then G is pancyclic. By using this result, we prove that if G is hamiltonian with order n ≥ 20 and if G has two nonadjacent vertices u and v such that d(u)+d(v) ≥ n+z, where z = 0 when n is odd and z = 1 otherwise, then G contains a cycle of length m for each 3 ≤ m ≤ max (d_C(u,v)+1, [(n+19)/13]), $d_C(u,v)$ being the distance of u and v on a hamiltonian cycle of G.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Faudree R.

1 Favaron O.

1 Flandrin E.

1 Li H.

1 1996

Wyniki wyszukiwania

Pancyclism and small cycles in graphs