Recursively find the path to all leaves descending from a given parent in a tree

I'm trying to write a query to identify the path to each furthest descendant of a particular parent node in a table of tree structures like:

0     1
	|	  |
	2	  3
    |	  |
	4	  5
   / \	  |
 *6*  8  *7*
  	  |
	 *9*

There are many parents, all children have one parent, parents have 0-5 children (but the graph is very "long" – most parents only have one child). There are no cycles. I'm trying to efficiently identify the path to the furthest descendants of a specific node (and not to any intermediate nodes). E.g. in the above: - get_leaf_paths(1) would return 1 row: {1, 3, 5, 7} - get_leaf_paths(2) would return 2 rows: {2, 4, 6} and {2, 4, 8, 9} Sample table:

CREATE TABLE graph (
    id bigint PRIMARY KEY,
    parent_id bigint,
    FOREIGN KEY (parent_id) REFERENCES graph(id)
);
INSERT INTO graph (id, parent_id)
	VALUES (0, NULL),
           (1, NULL),
           (2, 0),
           (3, 1),
           (4, 2),
           (5, 3),
           (6, 4),
           (7, 5),
           (8, 4),
		   (9, 8);

I'm hoping for a result that looks something like:

SELECT get_leaf_paths.* FROM get_leaf_paths(0);
path
-----
{0, 2, 4, 6}
{0, 2, 4, 8, 9}
(2 rows)

In my [initial attempt](https://dba.stackexchange.com/questions/289512/drop-intermediate-results-of-recursive-query-in-postgres) at a function with a recursive query, I've had trouble selecting only the furthest leaves, especially since some branches are shorter than others (e.g. 6 and 9 above are at different depths). The paths can be very deep (thousands or millions of elements), so I would also like to avoid the excessive memory usage of generating paths for every intermediate node. Any ideas would be greatly appreciated. Thanks!