Hadwiger conjecture
... that the Hadwiger conjecture implies that the surface of any three-dimensional convex body can be illuminated by only eight light sources, but the best proven bound is that 16 lights are sufficient?
... that the <b id="mwDew"><a href="./Hadwiger_conjecture_(combinatorial_geometry)" id="mwDe0" rel="mw:WikiLink" title="Hadwiger conjecture (combinatorial geometry)">Hadwiger conjecture</a></b> <i id="mwDe4">(diagram pictured)</i> implies that the surface of any <a href="./Solid_geometry" id="mwDe8" rel="mw:WikiLink" title="Solid geometry">three-dimensional</a> <a href="./Convex_body" id="mwDfA" rel="mw:WikiLink" title="Convex body">convex body</a> can be <a href="./Lighting" id="mwDfE" rel="mw:WikiLink" title="Lighting">illuminated</a> by only eight light sources, but the best <a href="./Mathematical_proof" id="mwDfI" rel="mw:WikiLink" title="Mathematical proof">proven</a> bound is that 16 lights are sufficient?