Jacqui was so eager to be born that she chose a date, June 18th, made up not only of two EVEN numbers but of two numbers also divisible by 3, (18,6). Though the latter divisor means that a Honeycomb Lattice Labyrinth is possible, I got pretty badly stuck drawing the missing links graph, but after several failed attempts it finally yielded. Here is the suitably energetic result for a birthdate shared with Paul McCartney and Delia Smith. Apologies for the rather garish coloration. My colour palette is in need of education.
It seems that there are indeed many different avenues open to those born on June 18th.