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Issue No. 04 - April (2009 vol. 58)
ISSN: 0018-9340
pp: 528-540
Jung-Heum Park , The Catholic University of Korea, Korea
Hee-Chul Kim , Hankuk University of Foreign Studies, Yongin-si
Hyeong-Seok Lim , Chonnam National University, Gwangju
A many-to-many k-disjoint path cover (k-DPC) of a graph G is a set of k disjoint paths joining k sources and k sinks in which each vertex of G is covered by a path. It is called a paired many-to-many disjoint path cover when each source should be joined to a specific sink, and it is called an unpaired many-to-many disjoint path cover when each source can be joined to an arbitrary sink. In this paper, we discuss about paired and unpaired many-to-many disjoint path covers including their relationships, application to strong Hamiltonicity, and necessary conditions. And then, we give a construction scheme for paired many-to-many disjoint path covers in the graph H_{0} \oplus H_{1} obtained from connecting two graphs H_{0} and H_{1} with |V(H_{0})| = |V(H_{1})| by |V(H_{0})| pairwise nonadjacent edges joining vertices in H_{0} and vertices in H_{1}, where H_{0} = G_{0} \oplus G_{1} and H_{1} = G_{2} \oplus G_{3} for some graphs G_{j}. Using the construction, we show that every m-dimensional restricted HL-graph and recursive circulant G(2^{m}, 4) with f or less faulty elements have a paired k-DPC for any f and k \geq 2 with f + 2k \leq m.
Fault tolerance, disjoint path covers, interconnection networks, restricted HL-graphs, recursive circulants, strong Hamiltonicity, fault Hamiltonicity.

H. Lim, J. Park and H. Kim, "Many-to-Many Disjoint Path Covers in the Presence of Faulty Elements," in IEEE Transactions on Computers, vol. 58, no. , pp. 528-540, 2008.
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