According to this excerpt from the book Covering Walks in Graphs by Fujie & Zhang (2014), the Zamfirescu graph of order 36¹ is non-traceable (i.e.: does not contain a Hamiltonian path). Moreover, this graph is a snark and hence 3-regular and 2-connected.

The Thomassen graph of order 34² is also 3-regular, 2-connected, and non-traceable.

1. Zamfirescu, Tudor. "On longest paths and circuits in graphs." Mathematica Scandinavica 38.2 (1976): 211-239.

2. Thomassen, Carsten. "Hypohamiltonian and hypotraceable graphs." Discrete Mathematics 9.1 (1974): 91-96.

According to this excerpt from the book Covering Walks in Graphs by Fujie & Zhang (2014), the Zamfirescu graph of order 36^[1] is non-traceable (i.e.: does not contain a Hamiltonian path). Moreover, this graph is a snark and hence 3-regular and 2-connected.

The Thomassen graph of order 34^[2] is also 3-regular, 2-connected, and non-traceable.

1. Zamfirescu, Tudor. "On longest paths and circuits in graphs." Mathematica Scandinavica 38.2 (1976): 211-239.

2. Thomassen, Carsten. "Hypohamiltonian and hypotraceable graphs." Discrete Mathematics 9.1 (1974): 91-96.

According to this excerpt from the book Covering Walks in Graphs by Fujie & Zhang (2014), the Zamfirescu graph of order 36 is non-traceable (i.e.: does not contain a Hamiltonian path). Moreover, this graph is a snark and hence 3-regular and 2-connected.

According to this excerpt from the book Covering Walks in Graphs by Fujie & Zhang (2014), the Zamfirescu graph of order 36¹ is non-traceable (i.e.: does not contain a Hamiltonian path). Moreover, this graph is a snark and hence 3-regular and 2-connected.

The Thomassen graph of order 34² is also 3-regular, 2-connected, and non-traceable.

1. Zamfirescu, Tudor. "On longest paths and circuits in graphs." Mathematica Scandinavica 38.2 (1976): 211-239.

2. Thomassen, Carsten. "Hypohamiltonian and hypotraceable graphs." Discrete Mathematics 9.1 (1974): 91-96.