4. The ten smallest positive odd numbers $1, 3, \cdots, 19$ are arranged on a circle. Let $m$ be the maximum value of the sum of any one of the ten numbers and its two adjacent numbers. Then the minimum value of $m$ is ( ).
(A) 31
(B) 32
(C) 33
(D) 34
4. C.

As shown in Figure 5, the ten numbers given on the circumference are divided into four parts: $S_{1}, S_{2}, S_{3}, S_{4}$, where $S_{1}$ contains only the number $1$, and $S_{2}, S_{3}, S_{4}$ each contain three adjacent numbers.

Thus, the sum of the nine numbers in $S_{2}, S_{3}, S_{4}$ is
$$
3+5+\cdots+19=99 \text{. }
$$

And $99 \div 3=33$, by the Pigeonhole Principle, we know that the value of $m$ is at least 33. The two arrangements shown in Figure 6 satisfy $m=33$.
Figure 6