Graph Coloring · Medium problem

Three managers $M_1,M_2,M_3$ and five employees $E_1,\ldots,E_5$ have a supervising link whenever a manager directly oversees an employee: $M_1$ oversees $E_1,E_2,E_3$; $M_2$ oversees $E_1,E_4$; $M_3$ oversees $E_5$. No manager oversees another manager, and no employee oversees another employee. Using König's edge-coloring theorem, what is the fewest meeting times needed so that no person attends two overlapping one-on-one meetings (two links sharing a person can't use the same time)?