What is the maximum number of nodes I can traverse in an undirected graph visiting each node exactly once? So I have an un-directed un-weighted graph. It contains cycles. I would like to find the path which visits the most nodes with no repeat visits to any node. Since this is a graph traversal, you can start and end at any node you like.
Background Research: I have looked at Travelling Salesman Problem (TSP); this problem is different and does NOT allow you to finish where you started from and there are no weights. I have looked at several other algorithms, but have found none suitable for this problem.
Graph Size: There are 100 nodes in the graph; with 10 disconnected nodes.
 A: This problem is still difficult, it is known as Hamiltonian path, and NP-complete. It doesn't really make a difference if the path is closed (a circuit) or not. Just ask the HAM-PATH problem for every pair of endpoints of all edges and you could solve HAM-CIRCUIT.
A: http://en.wikipedia.org/wiki/Longest_path_problem

In graph theory and theoretical computer science, the longest path
  problem is the problem of finding a simple path of maximum length in a
  given graph. A path is called simple if it does not have any repeated
  vertices; the length of a path may either be measured by its number of
  edges, or (in weighted graphs) by the sum of the weights of its edges.
  In contrast to the shortest path problem, which can be solved in
  polynomial time in graphs without negative-weight cycles, the longest
  path problem is NP-hard, meaning that it cannot be solved in
  polynomial time for arbitrary graphs unless P = NP. Stronger hardness
  results are also known showing that it is difficult to approximate.
  However, it has a linear time solution for directed acyclic graphs,
  which has important applications in finding the critical path in
  scheduling problems.

