INDEPENDENT CYCLES WITH LIMITED SIZE IN A GRAPH

Let k and s be two positive integers with s greater-than-or-equal-to 3. Let G be a graph of order n greater-than-or-equal-to sk. Write n = qk + r, 0 less-than-or-equal-to r less-than-or-equal-to k - 1. Suppose that G has minimum degree at least (s - 1)k. Then G contains k independent cycles C1, C2,..., C(k) such that s less-than-or-equal-to l(C(i)) less-than-or-equal-to q for 1 less-than-or-equal-to i less-than-or-equal-to k - r and s less-than-or-equal-to l(C(i)) less-than-or-equal-to q + 1 for k - r < i less-than-or-equal-to k, where l(C(i)) denotes the length of C(i).