We design a O(n3) polynomial time algorithm for finding a (k−1)– regular subgraph in a k–regular graph without any induced star Kk1,3(claw–free). A polynomial time algorithm for finding a cubic subgraph in a 4–regular locally connected graph is also given. A family of k–regular graphs with an induced star k1,3 (k even, k≥ 6), not containing any (k−1)–regular subgraph is also constructed.
