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- W2938165076 abstract "For the underlying graph G of a network, k spanning trees of G are called completely independent spanning trees (CISTs for short) if they are mutually inner-node-disjoint. It has been known that determining the existence of k CISTs in a graph is an NP-hard problem, even for $$k=2$$ . Accordingly, researches focused on the problem of constructing multiple CISTs in some famous networks. Pai and Chang [28] proposed a unified approach to recursively construct two CISTs with diameter $$2n-1$$ in several n-dimensional hypercube-variant networks for $$ngeqslant 4$$ , including locally twisted cubes $$LTQ_n$$ . Later on, they provided a new construction for $$LTQ_n$$ and showed that the diameter of two CISTs can be reduced to $$2n-2$$ if $$n=4$$ (and thus is optimal) and $$2n-3$$ if $$ngeqslant 5$$ . In this paper, we intend to construct more CISTs of $$LTQ_n$$ . We develop a novel tree searching algorithm, called two-stages tree-searching algorithm, to construct three CISTs of $$LTQ_6$$ and show that the three CISTs of the high-dimensional $$LTQ_n$$ for $$ngeqslant 7$$ can be constructed by recursion. The diameters of three CISTs for $$LTQ_n$$ we constructed are 9, 12 and 14 when $$n=6$$ , and are $$2n-3$$ , $$2n-1$$ and $$2n+1$$ when $$ngeqslant 7$$ ." @default.
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- W2938165076 date "2019-01-01" @default.
- W2938165076 modified "2023-09-27" @default.
- W2938165076 title "Constructing Three Completely Independent Spanning Trees in Locally Twisted Cubes" @default.
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- W2938165076 doi "https://doi.org/10.1007/978-3-030-18126-0_8" @default.
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