The 2-factor theorem is a result in graph theory, discovered by Julius Petersen and counted among the earliest works in the field. It states that if a graph is regular with an even degree 2k, then its edges can be partitioned into k edge-disjoint 2-factors, where a 2-factor is a spanning subgraph in which every vertex has degree two and which therefore decomposes into cycles that together touch every vertex exactly once. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementEvery regular graph whose degree is an even number 2k has its edges partitioned into k edge-disjoint 2-factors, where a 2-factor is a spanning subgraph in which every vertex has degree two. 1 Sources
1. 2-factor theorem (Wikipedia)
History section, first sentenceQuote, History section, first sentence
The theorem appears first in the 1891 article "Die Theorie der regulären graphs".
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