... proof of Theorem 1.2 shows that the value of n0 (k) in the statement of the theorem is O(k ) Another thing to note is that, as long as p ≥ 2, the actual value of p is insignificant Let C ∗ be the ... in G [A ] sharing a common endpoint in A Denote these two edges by (a 1 , a0 ) and (a0 , a1 ) As in the previous case we can obtain a Pk of the form a 1 , a0 , a1 , x1 , a2 , x2 , a3 , , ab−1 ... W.l.o.g a1 is a neighbor of x1 and ab+1 is a neighbor of xb As in the previous cases we can obtain a Pk of the form a0 , a1 , x1 , a2 , x2 , a3 , , ab−1 , xb−1 , ab , xb , ab+1 , ab+2 The only...