A clean-room implementation 11 of BFS in Elisp:
(defun my-breadth-first-graph-search (frontier neighbors goalp)
"Perform depth-first search (DFS) on a graph.
All arguments are like those for `my-graph-search', which see."
(let ((fifo #'nconc))
(my-graph-search frontier neighbors goalp fifo)))
(defalias 'my-bfs-graph-search #'my-breadth-first-graph-search)
Test.
graph {
bgcolor = transparent
node [shape = circle]
A B C D E F G I J K L
F [style = filled] # goal
A -- B
A -- C
A -- D
B -- E
B -- I
C -- F
D -- G
D -- L
E -- I
E -- J
G -- K
G -- L
}
(let ((graph '((a b c d)
(b a e i)
(c a f)
(d a g l)
(e b i j)
(f c)
(g d k l)
(i b e)
(j e)
(k g)
(l d g)))
(my-graph-search-debug t))
(princ (format "Solution: %s\n"
(my-dfs-graph-search
'((a))
(lambda (path) (alist-get (car path) graph))
(lambda (path) (eq (car path) 'f))))))
Search: (a) Search: (b a) Search: (e b a) Search: (j e b a) Search: (i b a) Search: (c a) Search: (f c a) Solution: (f c a)