Bipancyclic Properties of Faulty Hypercubes. (14th October 2012) - Hung, Chun-Nan; Hsiao, Min-Kun
Abstract : A bipartite graph G = ( V, E ) is bipancyclic if it contains cycles of every even length from 4 to | V | and edge bipancyclic if every edge lies on a cycle of every even length from 4 to | V | . Let Q n denote the n -dimensional hypercube. Let F be a subset of V ( Q n ) ∪ E ( Q n ) such that F can be decomposed into two parts F a v and F e, where F a v is a union of f a v disjoint adjacent pairs of V ( Q n ), and F e consists of f e edges. We prove that Q n - F is bipancyclic if f a v + f e ≤ n - 2 . Moreover, Q n - F is edge bipancyclic if f a v + f e ≤ n - 2 with f a v < n - 2 .