16. In a Cartesian coordinate system, there are 10 different points $P_{1}\left(x_{1}, y_{1}\right), P_{2}\left(x_{2}, y_{2}\right), \cdots, P_{10}\left(x_{10}, y_{10}\right)$. If $x_{i}=x_{j}$ or $y_{i}=y_{j}$, then $P_{i}$ and $P_{j}$ are called a "coordinate pair" (the order of $P_{i}$ and $P_{j}$ does not matter). If the 10 different points satisfy: the number of points that form a "coordinate pair" with each point does not exceed $m$; and in any case, they can be exactly divided into 5 pairs, none of which are "coordinate pairs". What is the maximum value of $m$?
Given 10 different points as $P_{1}(1,1), P_{2}(1,2), P_{3}(1,3), P_{4}(1,4), P_{5}(1,5), P_{6}(1,6)$, $P_{7}(2,2), P_{8}(2,3), P_{9}(2,4), P_{10}(2,5)$. Since $P_{1}(1,1), P_{2}(1,2), P_{3}(1,3), P_{4}(1,4), P_{5}(1,5), P_{6}(1,6)$ form "same-label point pairs" with each other, it is impossible to divide the 10 different points into 5 point pairs such that no point pair is a "same-label point pair". Therefore, $m \leqslant 4$. If $m \leqslant 4$, first randomly divide the 10 points into 5 point pairs: $\left(Q_{1}, R_{1}\right),\left(Q_{2}, R_{2}\right),\left(Q_{3}, R_{3}\right),\left(Q_{4}, R_{4}\right)$, $\left(Q_{5}, R_{5}\right)$. If there exists a "same-label point pair", such as $\left(Q_{1}, R_{1}\right)$, consider the following adjustments:
(1) Adjust $\left(Q_{1}, R_{1}\right),\left(Q_{2}, R_{2}\right)$ to $\left(Q_{1}, Q_{2}\right),\left(R_{1}, R_{2}\right)$, leaving the rest unchanged;
(2) Adjust $\left(Q_{1}, R_{1}\right),\left(Q_{2}, R_{2}\right)$ to $\left(Q_{1}, R_{2}\right),\left(R_{1}, Q_{2}\right)$, leaving the rest unchanged;
(3) Adjust $\left(Q_{1}, R_{1}\right),\left(Q_{3}, R_{3}\right)$ to $\left(Q_{1}, Q_{3}\right),\left(R_{1}, R_{3}\right)$, leaving the rest unchanged;
(4) Adjust $\left(Q_{1}, R_{1}\right),\left(Q_{3}, R_{3}\right)$ to $\left(Q_{1}, R_{3}\right),\left(R_{1}, Q_{3}\right)$, leaving the rest unchanged;
(5) Adjust $\left(Q_{1}, R_{1}\right),\left(Q_{4}, R_{4}\right)$ to $\left(Q_{1}, Q_{4}\right),\left(R_{1}, R_{4}\right)$, leaving the rest unchanged;
(6) Adjust $\left(Q_{1}, R_{1}\right),\left(Q_{4}, R_{4}\right)$ to $\left(Q_{1}, R_{4}\right),\left(R_{1}, Q_{4}\right)$, leaving the rest unchanged;
(7) Adjust $\left(Q_{1}, R_{1}\right),\left(Q_{5}, R_{5}\right)$ to $\left(Q_{1}, Q_{5}\right),\left(R_{1}, R_{5}\right)$, leaving the rest unchanged;
(8) Adjust $\left(Q_{1}, R_{1}\right),\left(Q_{5}, R_{5}\right)$ to $\left(Q_{1}, R_{5}\right),\left(R_{1}, Q_{5}\right)$, leaving the rest unchanged.

Since $Q_{1}, R_{1}$, except for $R_{1}, Q_{1}$, can form "same-label point pairs" with at most 3 other points each, one of the 8 methods above must result in two point pairs that are not "same-label point pairs". Thus, after one adjustment, the number of "same-label point pairs" is reduced by at least one. If there are still "same-label point pairs" after the adjustment, continue the adjustment. After a finite number of adjustments, it is certain that no point pair will be a "same-label point pair". In summary, the maximum value of $m$ is 4.