A Remark on Rainbow 6-Cycles in Hypercubes.
PARALLEL PROCESSING LETTERS(2018)
摘要
We call an edge-coloring of a graph G a rainbow coloring the edges of G are colored with distinct colors. For every even positive integer k >= 4, let f(n,k) denote the minimum number of colors required to color the edges of the n, dimensional cube Q(n), so that every copy of C-k is rainbow. Faudree et al. [6] proved that f(n, 4) = n, for n = 4 or n > 5. Mubayi et al. [8] showed that n <= f (n, 6) < n(1+o)(1). In this note, we show that f(n, 6) >= 2n - 1. Moreover, we obtain the number of 6-cycles of Q(n),
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关键词
Interconnection networks,hypercube,edge coloring,6-cycle,rainbow
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