A graph where the degrees of the vertices are 1 or 2, consists of only paths and cycles.
I know at least one problem where this turns out to be very useful:
Do you guys know other problems?
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Codeforces Round 976 (Div. 2) and Divide By Zero 9.0
17:13:33
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Codeforces Round 976 (Div. 2) and Divide By Zero 9.0
17:13:33
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