Could this be used to find the largest path in a graph?


Savitch’s theorem “test[s] the existence of a path from a vertex s to another vertex t that uses at most k edges”

Could this be used to find the largest path in a graph?

We know there’s a walk of length a from b to c. We can keep lowering a by 1 to find a d where there’s no walk from b to c. Now we know there’s a path of length d+1 between b and c. We can try other b and c to maximize d+1. Does this find the largest path in the graph?

What is my mistake?