Ring embedding in faulty pancake graphs

Abstract

In this paper, we consider the fault hamiltonicity and the fault hamiltonian connectivity of the pancake graph P-n. Assume that F subset of or equal to V(P-n) boolean OR E(P-n). For n greater than or equal to 4, we prove that P-n - F is hamiltonian if F less than or equal to (n - 3) and P-n - F is hamiltonian connected if F less than or equal to (n - 4). Moreover, all the bounds are optimal. (C) 2003 Elsevier Science B.V. All rights reserved.