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
On generalized middle-level problem
Information Sciences: an International Journal
A class of hierarchical graphs as topologies for interconnection networks
Theoretical Computer Science
Many-to-many n-disjoint path covers in n-dimensional hypercubes
Information Processing Letters
Computational complexity of long paths and cycles in faulty hypercubes
Theoretical Computer Science
Edge-fault-tolerant diameter and bipanconnectivity of hypercubes
Information Processing Letters
Efficient connectivity testing of hypercubic networks with faults
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Disjoint path covers in recursive circulants G(2m,4) with faulty elements
Theoretical Computer Science
Paired many-to-many disjoint path covers of hypercubes with faulty edges
Information Processing Letters
Paired many-to-many disjoint path covers of the hypercubes
Information Sciences: an International Journal
The 2-path-bipanconnectivity of hypercubes
Information Sciences: an International Journal
Single-source three-disjoint path covers in cubes of connected graphs
Information Processing Letters
Paired many-to-many disjoint path covers in faulty hypercubes
Theoretical Computer Science
| Hi-index | 0.02 |
Given a set $\pc=\{a_i,b_i\}_{i=1}^m$ of pairs of vertices in a graph $G$, is there a collection of paths $\{P_i\}_{i=1}^m$ such that $P_i$ connects $a_i$ with $b_i$ and $\{V(P_i)\}_{i=1}^m$ partitions $V(G)$? We study this problem for the graph $Q_n-\ff$ obtained from the $n$-dimensional hypercube $Q_n$ by removing a set $\ff$ of faulty vertices. We show that an obvious necessary condition for the existence of such a partition is also sufficient provided $2|\pc|+ 3|\ff|\le n-3$. As a corollary, we obtain a similar characterization for the existence of a hamiltonian cycle and a hamiltonian path of $Q_n-\ff$ provided $|\ff|\le(n-5)/3$. On the other hand, if the size of $\ff$ is not limited, the problems are NP-complete.