Triangle-free 2-matchings and M-concave functions on jump systems

As a quantitative extension of these results, we investigate a relationship between weighted Ck-free 2-matchings and M-concave functions on constant-parity jump systems. It is known that the weighted Ck-free 2-matchings induce an M-concave function on a constant-parity jump system for k≤2, and it is not always true for k≥4, which is consistent with the polynomial solvability of the maximization problem. In this paper, we show that the weighted C3-free 2-matchings induce an M-concave function on a constant-parity jump system.