The odd-ballooning of a graph F is the graph obtained from F by replacing each edge in F by an odd cycle of length between 3 and \(q\ (q\ge 3)\) where the new vertices of the odd cycles are all different. Given a forbidden graph H and a positive integer n, the extremal number, ex(n, H), is the maximum number of edges in a graph on n vertices that does not contain H as a subgraph. Erdös et al. and Hou et al. determined the extremal number of odd-ballooning of stars. Liu and Glebov determined the extremal number of odd-ballooning of paths and cycles respectively when replacing each edge of the paths or the cycles by a triangle. In this paper we determine the extremal number and find the extremal graphs for odd-ballooning of paths and cycles, when replacing each edge of the paths or the cycles by an odd cycle of length between 3 and \(q \ (q \ge 3)\) and n is sufficiently large.

的曲线图奇数气球˚F是从所得到的曲线图˚F通过替换在每个边缘˚F通过3之间的长度的奇数周期\（Q \（Q \ GE 3）\） ，其中奇数周期的新的顶点是都不同。给定一个禁忌图H和一个正整数n，极值ex（n，  H）是n个不包含H的顶点在图上的最大边数作为子图。Erdös等。和侯等人。确定了奇数气球膨胀的极值。当用三角形替换路径或循环的每个边时，Liu和Glebov分别确定了路径和循环的奇数膨胀的极值。在本文中，当用3到\（q \（q \ ge 3之间的长度的奇数循环）替换路径或循环的每个边时，我们确定极值数目并找到路径和循环的奇数气球的极值图。）\）并且n足够大。