Design-theoretic approach to the Earth-Moon problem: constructing biplanar graphs with small independence number / large fractional chromatic number, and proving structural obstructions from first principles.
We sharpen what counting arguments can certify in the Earth–Moon problem and reduce Král's independence-ratio question to a single local lemma. (i) A clique blo
A graph has outerthickness at most two if its edges are the union of two outerplanar graphs. Its largest chromatic number is known only to lie in $\{6,7,8\}$ (G
