Let G=(V,E) be a graph and let AG be the clique-vertex incidence matrix of G. It is well known that G is perfect iff the system AGx≤1, x≥0 is totally dual integral (TDI). In 1982, Cameron and Edmonds proposed to call G box-perfect if the system AGx≤1, x≥0 is box-totally dual integral (box-TDI), and posed the problem of characterizing such graphs. In this paper we prove the Cameron–Edmonds conjecture on box-perfectness of parity graphs, and identify several other classes of box-perfect graphs. We also develop a general and powerful method for establishing box-perfectness.
Publication Source (Journal or Book title)
Journal of Combinatorial Theory. Series B
Ding, G., Zang, W., & Zhao, Q. (2018). On box-perfect graphs. Journal of Combinatorial Theory. Series B, 128, 17-46. https://doi.org/10.1016/j.jctb.2017.07.001