A GENERALIZATION OF PETERSEN THEOREM

Petersen's theorem asserts that any cubic graph with at most 2 cut edg es has a perfect matching. We generalize this classical result by show ing that any cubic graph G = (V, E) with at most 1 cut edge has a T-jo in of cardinality less than or equal to Absolute value of V/2 for ever y even subset T of vertices. Our result is based on the Edmonds-Johnso n min-max relation for T-joins.