postgresql graph query and limitation

/*
We consider an oriented graph, with nodes ("+" : numbers) and arcs ( "-" : letters). Each arc is oriented from lowest node id to highest node id.
We want to follow the graph from node 1 to node 10, propagating through all arcs, and keeping all arcs just once in our results.
We want to keep the paths which we followed to each new visited arc.

The graph :

       +1
       |
       |A
   B   |
3+-----+2
 |     |
 |     |
C|     |E
 |     |
4+-----+5
   D   |
       |F
       |
   G   |
 7+----+6
  |    |I
  |H   |
  \----+8
       |
       | J
       |
       +9
       |
       |K
       |
       +10

Expected result :
A
A-B
A-E
A-B-C
A-E-F
A-B-C-D
A-E-F-G
A-E-F-I
A-E-F-G-H
A-E-F-I-J
A-E-F-I-J-K
( 11 rows )
*/

/* create our graph table */

drop table if exists graph;
create table graph (
id serial
, node_start int
, node_end int
, nam varchar
);

/* insert the data corresponding to the graph above */
insert into graph (node_start, node_end, nam)
values ( 1, 2, 'A'), (2, 3, 'B'), (3, 4, 'C'), (4, 5, 'D'), (2, 5, 'E'), (5, 6, 'F'), (6, 7, 'G'), (7, 8, 'H'), (6, 8, 'I'), (8, 9, 'J'), (9, 10, 'K');

/* check data */
select * from graph;

-- Follow the graph from 1 to 10 ( arc A to K )
-- We only keep node identifiers and use union to deduplicate

with recursive search_graph (id, node_end, nam) as (
select g.id, g.node_end, g.nam from graph as g where nam = 'A'
union
select g.id, g.node_end, g.nam from search_graph as sg join graph as g on sg.node_end = g.node_start
)
select * from search_graph limit 100;
-- 11 rows with visited nodes

-- We now want to keep the paths to visited nodes
with recursive search_graph (id, node_end, nam, path, depth) as (
-- start data set : arc A
select g.id, g.node_end, g.nam, ARRAY[g.nam] as path, 1 as depth from graph as g where nam = 'A'
-- Recursive part
-- Since the path is distinct for every new line, union does not deduplicate any longer
-- we have to filter further on each recursion/iteration to deduplicate
union
select g.id, g.node_end, g.nam, sg.path || g.nam as path, depth + 1 as depth from search_graph as sg join graph as g on sg.node_end = g.node_start
)
select * from search_graph limit 100;

-- This is the query we would expect to work
with recursive search_graph (id, node_end, nam, path, depth) as (
-- same data set as start : arc A
select g.id, g.node_end, g.nam, ARRAY[g.nam] as path, 1 as depth from graph as g where nam = 'A'
-- union does not deduplicate since we have the path
union
-- in the following line, PostgreSQL raises an error :
-- ERROR:  recursive reference to query "search_graph" must not appear within a subquery
-- we could also use a "left join is null" structure, but PostgreSQL prevents the recursive CTE to be used in an outer join
select g.id, g.node_end, g.nam, sg.path || g.nam as path, depth + 1 as depth from search_graph as sg join graph as g on sg.node_end = g.node_start and g.id not in (select id from search_graph)
)
select * from search_graph limit 100;