3-connected configurations (n3) with no Hamiltonian circuit

Abstract

For more than a century there have been examples of (n3) configurations without a Hamiltonian circuit. However, all these examples were only 2-connected. It has been believed that all geometric 3-connected configurations (n3) admit Hamiltonian circuits. We present a 3-connected configuration (253) of points and lines in the Euclidean plane which has no Hamiltonian circuit.