... shows that the value of n0(k) in the statement of the theorem isO(k2). Another thing to note is that, as long as p ≥ 2, the actual value of p is insignificant.Let C∗be the family of even ... (however, for these wealready have the sharp result of Theorem 1.2), but there are many others. One example is the balanced double star Sk,k, that is obtained by taking two disjoint copies of the star ... ,ab−1,xb−1,ab,xb,ab+1,ab+2. The only remaining case is that k is odd and G[A] contains two or more independent edges,and all the endpoints of these independent edges are connected to a single vertex of B,say,x1....