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?