0 votes 0 votes How DFS(Depth First Search) modification is used to find whether a graph is planar or not ? Algorithms depth-first-search algorithms graph-algorithms shai-simonson + – ankitgupta.1729 asked Mar 21, 2018 ankitgupta.1729 1.3k views answer comment Share Follow See all 16 Comments See all 16 16 Comments reply Show 13 previous comments ankitgupta.1729 commented May 2, 2018 reply Follow Share I am confused that here linear means O(V) or O(E)..according to above video of prof Shai Simonson , linear means O(V) and in the paper of Hopcraft-Tarjan, they have taken adjacency list. may be that's why it is O(V) because adjacency list is for sparse graphs where E = O(V)...but according to wikipedia , DFS takes linear time in the size of the graph ie O(E).. 0 votes 0 votes srestha commented May 3, 2018 reply Follow Share @ankit I got that DFS works for linear time, if it is in place algo, otherwise not https://cs.stackexchange.com/questions/79934/lower-bound-on-space-of-dfs-keeping-the-running-time-linear https://arxiv.org/abs/1803.04282 0 votes 0 votes ankitgupta.1729 commented May 3, 2018 reply Follow Share @srestha , yes , everywhere ,it is written that DFS/BFS takes linear time ie O(m+n) but I m not getting that it is linear in terms of no. of nodes or no. of edges..because if graph is dense then m = O(n2) then time complexity of dfs becomes O(n2) which is not linear time in terms of no. of nodes..but in above video , sir said , it takes linear time in terms of no. of nodes..that's why I m confused. in ur link https://arxiv.org/abs/1803.04282 , they also said O(m+n) as linear time... 0 votes 0 votes Please log in or register to add a comment.