A111916 Number of Yutsis graphs or cubic dual Hamiltonian graphs on 2n nodes.

1, 2, 5, 18, 80, 475, 3836, 39555, 495045, 7159696, 116040456, 2068782009, 40107422184, 838931116609

Offset: 2

Author

Dries Van Dyck (VanDyck.Dries(AT)Gmail.com), Mar 05 2006

Keywords

• nonn
• more

Comments

Connected cubic graphs on 2n nodes which can be partitioned into two vertex induced trees which are necessarily of the same size.

They are called dual Hamiltonian because the cut separating both trees contains n+2 edges, corresponding to a Hamiltonian cycle in the planar dual if the graph is planar.

Maximal connected cubic graphs in the size of the largest vertex induced forest (floor((6*n-2)/4) nodes for a cubic graph on 2n nodes).

References

• F. Jaeger, On vertex-induced forests in cubic graphs, Proceedings 5th Southeastern Conference, Congressus Numerantium (1974) 501-512.
• A. P. Yutsis, I. B. Levinson and V. V. Vanagas, Mathematical Apparatus of the Theory of Angular Momentum, Israel Program for Scientific Translation, Jerusalem, 1962.

Links

• Dries Van Dyck and Veerle Fack, Yutsis Project
• D. Van Dyck, G. Brinkmann, V. Fack and B. D. McKay, To be or not to be Yutsis: algorithms for the decision problem, Computer Physics Communications 173 (2005) 61-70.