1. (15 pts, 3 ea.) Consider the following graph G with nodes {1, 2, 3, 4, 5, 6}:
In the following, s means node 1 and t means node 6, as indicated in the figure. State
whether or not each of the following is true, and provide a brief explanation.
(a) $(G, s, t, 2) \in \text{SPATH}$.
(b) $(G, s, t, 6) \in \text{LPATH}$.
(c) $(G, s, t) \in \text{UHAMPATH}$.
(d) $(G) \in \text{HC}$.
(e) $(G, 3) \in \text{VC}$.