Given a graph G with N nodes we need to find if cycle of length 100 exists.
I've been told that this problem is NP-Complete and can be reduced to the Hamiltonian Cycle problem. I believe this is just P.
My first thought was just to perform a DFS on each node with a max depth of 101 nodes and check if the last node equals the first. Given a starting node you have at most (n-1) nodes connected to it we need to search. That node has at most(n-2) nodes connected to it we need to search. Thus for each starting node we have a time complexity of O(n^101). Multiply by the number of nodes we need to do this over and we have O(n^102).
Am I correct or did I get something wrong here?