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Jul 4 at 12:33 vote accept Dominic van der Zypen
Jul 4 at 10:30 history became hot network question
Jul 4 at 9:52 answer added bof timeline score: 6
Jul 4 at 9:33 comment added bof @LouisEsperetHow does that follow? The OP's graph doesn't have to be double-critical, does it? There need only be one pair of adjacent vertices whose removal lowers the chromatic number by $2$.
Jul 4 at 6:49 comment added Louis Esperet If the "double-critical graph conjecture" openproblemgarden.org/op/double_critical_graph_conjecture is correct, the answer to the question is no.
Jul 4 at 2:28 history asked Dominic van der Zypen CC BY-SA 4.0