I have a simple theoretical question in very basic algorithms, as the title mentions, is it always true that the depth of BFS is $\leq$ DFS?
From what I understand, the tricky part here is the possible cycles in the graph. Even though that I believe that the depth of BFS will always be less or equal to the depth of DFS.
In each iteration of BFS, from what I understand, the depth might grow by one, but DFS's grows in each vertex it can not reach, sometimes above the maximal value of BFS.
So, is it always true that the depth of BFS is $\leq$ DFS?