  An irreducible element of a commutative ring is absolutely irreducible if no
power of it has more than one (essentially different) factorization into
irreducibles. In the case of the ring $\text{Int}(D)=\{f\in K[x]\mid
f(D)\subseteq D\}$, of integer-valued polynomials on a principal ideal domain
$D$ with quotient field $K$, we give an easy to verify graph-theoretic
sufficient condition for an element to be absolutely irreducible and show a
partial converse: the condition is necessary and sufficient for polynomials
with square-free denominator.
