Check whether BST contains Dead End or not

Given a Binary search Tree that contains positive integer values greater then 0. The task is to check whether the BST contains a dead end or not. Here Dead End means, we are not able to insert any element after that node.

Examples:

Input :        8
             /   \ 
           5      9
         /   \
        2     7
       /
      1               
Output : Yes
Explanation : Node "1" is the dead End because
         after that we cant insert any element.       

Input :       8
            /   \ 
           7     10
         /      /   \
        2      9     13

Output : Yes
Explanation : We can't insert any element at node 9.  

class Solution {
    public boolean bstDeadEnd(Node node, int min, int max) {
        if (node == null)
            return false;
        if (node.data == min && node.data == max)
            return true;
        return bstDeadEnd(node.left, min, node.data - 1) || bstDeadEnd(node.right, node.data + 1, max);
    }

    public boolean deadEnd(Node node) {
        // As the given BST can only have positive Integers
        return bstDeadEnd(node, 1, Integer.MAX_VALUE);
    }
}