Pancyclicity of 4-connected claw-free bull-free graphs

A graph G is said to be pancyclic if G contains cycles of lengths from 3 to vertical bar V(G)vertical bar. The bull B(i, j) is obtained by associating one endpoint of each of the path Pi+1 and Pj+1 with distinct vertices of a triangle. In [M. Ferrara et al., Discrete Math. 313 (2013), 460-467], it was shown that every 4-connected {K-1,K-3, B(i, j)}-free graph with i+j = 6 is pancyclic. In this paper we show that every 4-connected {K-1,K-3, B(i, j)}-free graph with i+j = 7 is either pancyclic or it is the line graph of the Petersen graph.