Hypohamiltonian snarks
Last update: 15 Dec 2020 | Contains: 42285 graphs
A snark is a connected bridgeless cubic graph (i.e., a biconnected cubic graph) with edge chromatic number of four (i.e. it cannot be properly edge-coloured using 3 colours). Snark is hypohamiltonian if it does not itself have a Hamiltonian cycle but every graph formed by removing a single vertex from it is Hamiltonian. The following collection was calculated by the House of Graphs (source) and lists all hypohamiltonian snarks on up to 36 vertices.
OEIS: A218880