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

Abstract

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.