In [6] the author defined a new property of graphs namely the edge-toughness. It was
proved in [6] that a 2t-tough graph is always t-edge-tough. It is proved in the present
paper that this is not true for (2t - epsilon)-tough graphs if t is a positive integer.
A result of Enomoto et al. in [5] implies that every 2-tough graph has a 2-factor.
In the present paper it is proved that every 1-edge-tough graph has a 2-factor. This
is a sharpening of the previous statement.
