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math.CO2026
The crossing number and the unit-distance crossing number of the Hamming graphs H(d,3)=K_3^{box d}, and their realizations over many coordinate fields
Haroldo Costa Silva Filho
The Hamming graph H(d,3)=K_3^{box d} (n=3^d vertices) is the graph of single-symbol errors of ternary codes, yet we ask a geometric question of it: can it be drawn in the plane wit…
math.CO2026
Exact certification of the coordinate fields of the triangle-free Exoo-Ismailescu unit-distance graphs EI17 and EI19 (HoG 51375, 51376): a solvable-non-solvable dichotomy (origami vs. S20) and the Laman-number conjecture
Haroldo Costa Silva Filho
We certify, exactly, the coordinate fields of a faithful planar realization of two neighbouring triangle-free Exoo-Ismailescu unit-distance graphs (UDGs), and show they realize the…