Abstract
In this note, we consider a minimum degree condition for a hamiltonian graph to have a 2-factor with two components. Let G be a graph of order n ⩾ 3 . Dirac's theorem says that if the minimum degree of G is at least 1 2 n , then G has a hamiltonian cycle. Furthermore, Brandt et al. [J. Graph Theory 24 (1997) 165–173] proved that if n ⩾ 8 , then G has a 2-factor with two components. Both theorems are sharp and there are infinitely many graphs G of odd order and minimum degree 1 2 ( | G | - 1 ) which have no 2-factor. However, if hamiltonicity is assumed, we can relax the minimum degree condition for the existence of a 2-factor with two components. We prove in this note that a hamiltonian graph of order n ⩾ 6 and minimum degree at least 5 12 n + 2 has a 2-factor with two components.
Published Version
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