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Paired Many-to-Many Disjoint Path Covers in Recursive Circulants $(G(2^m,4))$

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2 Author(s)
Sook-Yeon Kim ; Dept. of Comput. & Web Inf. Eng., Hankyong Nat. Univ., Anseong, South Korea ; Jung-Heum Park

A disjoint path cover (DPC for short) of a graph is a set of disjoint paths that cover all the vertices of the graph. A paired many-to-many k-DPC is a DPC composed of k paths between k sources and k sinks, such that each source is joined to a designated sink. We show that recursive circulant G(2m,4) with at most f faulty vertices and/or edges being removed has a paired many-to-many k-DPC joining k arbitrary sources and sinks for any f and k ≥ 2, subject to f+2k ≤ m+1, where m ≥ 5. The bound m+1 on f+2k is the best possible.

Published in:

Computers, IEEE Transactions on  (Volume:62 ,  Issue: 12 )

Date of Publication:

Dec. 2013

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