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Regular graph
Task number: 4173
Show that if the 2k-regular graph has an even number of edges, then either k or |VG| is even.
Solution
If we count the degrees, we get twice the total number of edges, that is |EG|=2k|VG|2=k|VG|.
If both factors were odd, we would get an odd number of edges, which would contradict the assumptions.
