Island Exploration
All The Best Cowboys

Jack, Kate, Locke and Boone searched for Claire on two different paths.  Michael was searching for Claire, alone, on the other side of the island. Locke sent him South.

While out on the trek, Locke ripped pieces of a red shirt to tie on tries so they could find their way back.  After  Locke and Boone split up from Kate and Jack they stumbled upon a strange object buried in the ground that appeared to be some sort of door or hatch.