Edge-fault-tolerant edge-bipancyclicity of bubble-sort graphs

The bubble-sort graph B n is a bipartite graph. Kikuchi and Araki [Edge-bipancyclicity and edge-fault-tolerant bipancyclicity of bubble-sort graphs. Information Processing Letters, 100, 52.59 (2006)] have proved that B n is edge-bipancyclic for n . 5 and B n . F is bipancyclic when n . 4 and |F| . n . 3. In this paper, we improve this result by showing that for any edge set F of B n with |F| . n . 3, every edge of B n .F lies on a cycle of every even length from 6 to n! for n . 5 and every edge of B n . F lies on a cycle of every even length from 8 to n! for n = 4