Before revision:  The size k of a MPC is also called the width of G. Computing a MPC is a basic problem, dating back to Dilworth's and Fulkerson's results in the 1950s, and is solvable in quadratic time in the worst case.
After revision:  The size k of a MPC is also called the width of G. Computing a MPC is a basic problem, dating back to Dilworth's and Fulkerson's results in the 1950s, and is doable in quadratic time in the worst case.