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Jun 8, 2022 at 11:06 comment added vidyarthi @verret yes, it is the set of $3$-cycles
Jun 7, 2022 at 4:28 comment added kabenyuk @vidyarthi Yes, almost so. For every $n\geq3$ in the graph $AG_n$ in this paper, $2n - 4$ mutually independent Hamiltonian cycles are explicitly constructed. Note the definitions.
Jun 6, 2022 at 18:36 comment added verret Can you clarify what is $S$? Is it the set of $3$-cycles?
Jun 6, 2022 at 17:35 comment added vidyarthi @kabenyuk As I seethe paper at first glance, it seems the answers are affirmative to my questions. Is this right?
Jun 6, 2022 at 15:27 history edited YCor CC BY-SA 4.0
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Jun 6, 2022 at 15:06 comment added kabenyuk It seems to me that all your questions can be answered by H.Su, S.-Y.Chen, S.-S.Kao, (2011). Mutually independent Hamiltonian cycles in alternating group graphs, The Journal of Supercomputing, 61(3), 560-571.
Jun 6, 2022 at 14:46 history edited vidyarthi CC BY-SA 4.0
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Jun 6, 2022 at 11:58 history asked vidyarthi CC BY-SA 4.0