  In 1985, Dunwoody showed that finitely presentable groups are accessible.
Dunwoody's result was used to show that context-free groups, groups
quasi-isometric to trees or finitely presentable groups of asymptotic dimension
1 are virtually free. Using another theorem of Dunwoody of 1979, we study when
a group is virtually free in terms of its Cayley graph and we obtain new proofs
of the mentioned results and other previously depending on them.
