A Graph Theorist Plants a Tree

A graph theorist, while planting a tree, is inspired to study coloring problems for a class of graphs. Namely, she completely determines the chromatic number for certain Cayley graphs associated to the cross product of the integers with itself finitely many times, modulo a cyclic subgroup. This result she dubs the "Tree Guard Theorem." She finds examples "in nature" of this theorem in action, and then seeds are sown for new directions to pursue.