Theoretical Computer Science ( IF 1.1 ) Pub Date : 2021-07-29 , DOI: 10.1016/j.tcs.2021.07.030 Yuxing Yang 1, 2 , Jing Li 3
The n-dimensional hypercube is one of the most attractive interconnection networks for multiprocessor systems and it is a bipartite graph. Let be a set of the end-nodes of k independent edges in and be a set of f edges in . Given a linear forest L of , in this paper, we prove that (i) admits a hamiltonian cycle passing through L if ; and for any two nodes x and y of the opposite partite sets in such that none of the paths in L has x or y as internal node or both of them as end-nodes, admits a hamiltonian path between x and y passing through L if ; and for any two distinct nodes u and v of the partite set not containing w in such that none of the paths in L has u or v as internal node or both of them as end-nodes, admits a hamiltonian path between u and v passing through L if , where w is an arbitrary node in .
中文翻译:
超立方体的混合容错规定的超哈密顿可解性
在ñ维超立方体是多处理器系统最有吸引力的互连网络之一,它是一个二部图。让是k 个独立边的端节点的集合 和 是一组f边. 给出的线性森林大号的, 在本文中,我们证明 ( i )承认一个通过L的汉密尔顿循环,如果; 和对于相反部分的任意两个节点x和y使得没有路径在大号具有X或ÿ作为内部节点或它们两者为端节点的,承认x和y之间通过L的哈密顿路径,如果; 和对于任何两个不同的节点ù和v不含有三方组的瓦特在使得没有在路径中的大号具有ü或v为内部节点或它们两者为端节点的,承认u和v之间通过L的哈密顿路径,如果,其中w是任意节点.