On the edge-hyper-Hamiltonian laceability of balanced hypercubes
Jianxiang Cao, Lihua Feng, Minyong Shi · Discussiones Mathematicae Graph Theory · 2016
The balanced hypercube BH n , defined by Wu and Huang, is a variant of the hypercube network Q n , and has been proved to have better properties than Q n with the same number of links and processors. For a bipartite graph G = (V 0 V 1 , E), we say G is edge-hyper-Hamiltonian laceable if it is Hamiltonian laceable, and for any vertex v V i , i {0, 1}, any edge e E(Gv), there is a Hamiltonian path containing e in Gv between any two vertices of V 1-i . In this paper, we prove that BH n is edge-hyper-Hamiltonian laceable.