Abstract
We design a O(n3 ) polynomial time algorithm for finding a (k -1)- regular subgraph in a k -regular graph without any induced star K 1,3 (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 K 1,3 (k even, k ≥ 6) , not containing any (k -1)-regular subgraph is also constructed.
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