Given a graph H, the Turán function ex (n, H) is the maximum number of edges in a graph on n vertices that does not contain H as a subgraph. Let s, t be integers and let H s, t be a graph consisting of s triangles and t cycles of odd lengths at least 5 which intersect in exactly one common vertex. Erdős et al.(1995) determined the Turán function ex (n, H s, 0) and the corresponding extremal graphs. Recently, Hou et al.(2016) determined ex (n, H 0, t) and the extremal graphs, where the t cycles have the same odd length q with q⩾ 5. In this paper, we further determine ex (n, H s, t) and the extremal graphs, where s⩾ 0 and t⩾ 1. Let ϕ (n, H) be the smallest integer such that, for all graphs G on n vertices, the edge set E (G) can be partitioned into at most ϕ (n, H) parts, of which every part either is a single edge or forms a graph isomorphic to H. Pikhurko and Sousa conjectured that ϕ (n, H)= ex (n, H) for χ (H)⩾ 3 and all sufficiently large n. Liu and Sousa (2015) verified the conjecture for H s, 0. In this paper, we further verify Pikhurko and Sousa’s conjecture for H s, t with s⩾ 0 and t⩾ 1.