Long cycles in certain graphs of large degree
Pak‐Ken Wong · International Journal of Mathematics and Mathematical Sciences · 2000
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(n2). In case G is 2‐connected, the condition |X| ≥ 3 can be removed and G is hamiltonian.