Fault-free Hamiltonian cycles passing through a linear forest in ternary n-cubes with faulty edges

Authors:
Yuxing Yang;Shiying Wang
Affiliations:
School of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, PR China;School of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, PR China and School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, PR China
Venue:
Theoretical Computer Science
Year:
2013

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Abstract

A linear forest in a graph is a subgraph each component of which is a path. In this paper, we investigate the existence of a Hamiltonian cycle passing through a linear forest in a ternary n-cube Q"n^3 (n=2) with faulty edges. Let F be a faulty edge set of Q"n^3 and L be a prescribed linear forest in Q"n^3-F. If |E(L)|@?2n-1 and |F|@?n-(@?|E(L)|/2@?+1), then there is a Hamiltonian cycle passing through L in Q"n^3-F.