Many-to-Many Disjoint Path Covers in Hypercube-Like Interconnection Networks with Faulty Elements
IEEE Transactions on Parallel and Distributed Systems
The two-equal-disjoint path cover problem of Matching Composition Network
Information Processing Letters
Information Processing Letters
Partitions of Faulty Hypercubes into Paths with Prescribed Endvertices
SIAM Journal on Discrete Mathematics
Edge-fault-tolerant bipanconnectivity of hypercubes
Information Sciences: an International Journal
Long paths in hypercubes with conditional node-faults
Information Sciences: an International Journal
Many-to-Many Disjoint Path Covers in the Presence of Faulty Elements
IEEE Transactions on Computers
Many-to-many disjoint paths in faulty hypercubes
Information Sciences: an International Journal
Long paths in hypercubes with a quadratic number of faults
Information Sciences: an International Journal
Unpaired many-to-many vertex-disjoint path covers of a class of bipartite graphs
Information Processing Letters
Many-to-many n-disjoint path covers in n-dimensional hypercubes
Information Processing Letters
Edge-fault-tolerant diameter and bipanconnectivity of hypercubes
Information Processing Letters
Paired many-to-many disjoint path covers of the hypercubes
Information Sciences: an International Journal
Paired many-to-many disjoint path covers in faulty hypercubes
Theoretical Computer Science
Hi-index | 0.89 |
Let M"k={u"i,v"i}"i"="1^k be a set of k pairs of distinct vertices of the n-dimensional hypercube Q"n such that it contains k vertices from each class of bipartition of Q"n. Gregor and Dvorak proved that if n2k, then there exist k vertex-disjoint paths P"1,P"2,...,P"k containing all vertices of Q"n, where two end-vertices of P"i are u"i and v"i for i=1,2,...,k. In this paper we show that the result still holds if removing n-2k-1 edges from Q"n. When k=2, we also show that the result still holds if removing 2n-7=1 edges from Q"n such that every vertex is incident with at least three fault-free edges, and the number 2n-7 of faulty edges tolerated is sharp.