Assume G is a $r$-regular bigraph, r$\ge$1.
Show that
a) G admits a 1-factor
b) the edge chromatic number of G is r;in other words, G can be decomposed into 1-factor.
I think I can use the Marriage theorem. Here is the definition:
For part a), I would like to state that G has equal size of W and W', so we can produce a matching which covers the left part and the right part. Is this enought to show G admits a 1-factor?
Also, does a) and b) mean the same thing?