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Dec 28, 2022 at 14:49 comment added Fedor Petrov @GerryMyerson that's an example of what is mentioned in the pre-last paragraph. But a more involved group theory result would be highly appreciated.
Dec 28, 2022 at 14:37 comment added Gerry Myerson Maybe this example is too simple to post as an answer: Given a group of even order, form the graph with an edge joining each element to its inverse. The identity element is unpaired, so there must be at least one more unpaired element; thus, the group must have an element of order two.
Jun 14, 2021 at 7:52 history edited Fedor Petrov CC BY-SA 4.0
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Mar 1, 2019 at 18:33 history edited darij grinberg CC BY-SA 4.0
empty graphs work fine here
Mar 1, 2019 at 17:50 history edited Fedor Petrov CC BY-SA 4.0
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Jan 14, 2018 at 13:16 history made wiki Post Made Community Wiki by Todd Trimble
Jan 14, 2018 at 2:35 history edited YCor
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Oct 12, 2011 at 16:04 answer added Timothy Chow timeline score: 8
Oct 12, 2011 at 12:34 answer added Tony Huynh timeline score: 4
Oct 12, 2011 at 10:40 history edited Fedor Petrov CC BY-SA 3.0
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Oct 12, 2011 at 10:11 answer added Gjergji Zaimi timeline score: 11
Oct 12, 2011 at 8:53 history edited Fedor Petrov
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Oct 12, 2011 at 8:33 history asked Fedor Petrov CC BY-SA 3.0