A note on 1-factors in graphs

Conditions on a graphG are presented which are sufficient to guarantee thatG–Z contains a 1-factor, whereZ is a set of edges ofG of restricted cardinality. These conditions provide generalizations of several known results and, further, establish the result that ifG is anr-regular, (r–2)-edge-connected graph (r2) of even order andz is an integer with 0zr–1 such thatG contains fewer thanr–z edge cut sets of cardinalityr–2, thenG–Z has a 1-factor for each setZ ofz edges ofG.