Talk:Graph factorization

This is a stub

This article is a stub. Please add history, uses, importance, etc...--Cronholm144 22:45, 12 May 2007 (UTC)[reply]

Looking for a possible interlang for this page-

to someone who reads German better than I, does de:Einfacher Graph cover the same material? Schissel | Sound the Note! 14:22, 17 February 2008 (UTC)[reply]

That article is describing simple undirected graphs. The main article on matching is de:Paarung (Graphentheorie), which defines k-Faktor. There is also a dab page de:k-Faktor. Michael Slone (talk) 16:11, 17 February 2008 (UTC)[reply]

2-factorizations - repeated results?

What's the second paragraph trying to say? It talks about a graph being "k-factored" but then chooses each of the two factors. If this is talking about 2-factorizations, it's just repeating the results of the first paragraph (and adding the extra "connected" condition which is not relevant). If it is talking about k-factorizations then I believe it's in the wrong section.

William Pettersson (talk) 02:36, 12 September 2013 (UTC)[reply]

1-factorization

If a graph is 1-factorable, then it has to be a regular graph. -- This is just wrong; see the example pictures in the Matching article.DerPhimor (talk) 13:24, 10 September 2015 (UTC)[reply]

No. I believe you're confusing the existence of a 1-factor with the existence of a 1-factorization. A 1-factor is just a perfect matching and for that to exist, indeed, the graph need not be regular. But a 1-factorization is a partition of the whole graph into perfect matchings, so all vertices need to have the same degree (equal to the number of perfect matchings), or else there would be extra left over edges at some vertices. —David Eppstein (talk) 16:10, 10 September 2015 (UTC)[reply]

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