  A class of simple graphs such as ${\cal G}$ is said to be {\it
odd-girth-closed} if for any positive integer $g$ there exists a graph $G \in
{\cal G}$ such that the odd-girth of $G$ is greater than or equal to $g$. An
odd-girth-closed class of graphs ${\cal G}$ is said to be {\it odd-pentagonal}
if there exists a positive integer $g^*$ depending on ${\cal G}$ such that any
graph $G \in {\cal G}$ whose odd-girth is greater than $g^*$ admits a
homomorphism to the five cycle (i.e. is $C_{_{5}}$-colorable).
  In this article, we show that finding the odd girth of generalized Petersen
graphs can be transformed to an integer programming problem, and using this we
explicitly compute the odd girth of such graphs, showing that the class is
odd-girth-closed. Also, motivated by showing that the class of generalized
Petersen graphs is odd-pentagonal, we study the circular chromatic number of
such graphs.
