The method of extremal structure on the k-maximum cut problem

摘要

Using the Method of Extremal Structure, which combines the use of reduction rules as a preprocessing technique and combinatorial extremal arguments, we will prove the fixed-parameter tractability and find a problem kernel for k-MAXIMUM CUT. This kernel has 2k edges, the same as that found by Mahajan and Raman in (Mahajan & Raman 1999), but using our methodology we also find a bound of k vertices leading to a running time of O(k 2^k/2 + n²).