Tessellate S.T.E.M.S - Computer Science - College - Set 2 - Problem 4

Let SPATH = $\{\langle G,k\rangle \mid G$ contains a path of length at most $k\}$ be a language and similarly LPATH = $\{\langle G,k\rangle \mid G$ contains a path of length at least $k\}$ .

Assuming $P \neq NP$ , which of the following is not true?

1. $SPATH\in P$
2. $LPATH \in NP$
3. There is a polynomial time many one reduction from $SPATH$ to $LPATH$
4. There is a polynomial time many one reduction from $LPATH$ to $SPATH$
5. LPATH is $NP$ -complete

This problem is a part of Tessellate S.T.E.M.S.