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I am working on Ramanujan graphs and have encountered something that needs a suggestion. Does the girth of a Ramanujan graph change if I delete one random edge from the graph?
The question can also be as follows: are there at least two edge-disjoint shortest cycles in Ramanujan graphs? If yes, the girth does not change if I delete some random edge.

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  • $\begingroup$ do you mean "arbitrary" instead of "random"? $\endgroup$ Jul 12, 2023 at 6:03
  • $\begingroup$ yes I meant arbitrary. $\endgroup$ Jul 13, 2023 at 4:52

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