Abstract
We raise the conjecture that every 3-regular digraph, except the digraphs D73, D83 and D2n2 for every integer n≥2, which are defined in the introduction of the paper, contains two vertex disjoint directed cycles of different lengths and give support for this conjecture by proving that every 3-regular digraph of girth 4 contains two vertex disjoint directed cycles of different lengths.
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