Long cycles in certain graphs of large degree

Pak-Ken Wong

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 24, 1-7

Abstract:

Let G be a connected graph of order n and X = { x ∈ V : d ( x ) ≥ n / 2 } . Suppose | X | ≥ 3 and G satisfies the modified Fan's condition. We show that the vertices of the block B of G containing X form a cycle. This generalizes a result of Fan. We also give an efficient algorithm to obtain such a cycle. The complexity of this algorithm is O ( n 2 ) . In case G is 2 -connected, the condition | X | ≥ 3 can be removed and G is hamiltonian.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:343142

DOI: 10.1155/S0161171200003653

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