I heard that the Petersen graph is a good test of a graph theory conjecture. As in, if you want to know whether a graph theory conjecture is false, the Petersen graph is likely to be a counterexample. So, with that in mind, are there any "reasonable" and "natural" graph theory conjectures, which is false, but for which the Petersen graph is NOT a counterexample? I would like a list of several such conjectures. Note, I do not have a formal definition of "reasonable" or "natural", but I know it when I see it.
2026-04-03 15:59:52.1775231992
Any "reasonable" and "natural" false graph theory conjectures for which the Petersen graph is not a counterexample?
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