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%I #14 May 06 2021 16:17:05
%S 1,2,5,18,80,475,3836,39555,495045,7159696,116040456,2068782009,
%T 40107422184,838931116609
%N Number of Yutsis graphs or cubic dual Hamiltonian graphs on 2n nodes.
%C Connected cubic graphs on 2n nodes which can be partitioned into two vertex induced trees which are necessarily of the same size.
%C 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.
%C 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).
%D F. Jaeger, On vertex-induced forests in cubic graphs, Proceedings 5th Southeastern Conference, Congressus Numerantium (1974) 501-512.
%D 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.
%H Dries Van Dyck and Veerle Fack, <a href="http://caagt.ugent.be/yutsis">Yutsis Project</a>
%H D. Van Dyck, G. Brinkmann, V. Fack and B. D. McKay, <a href="https://doi.org/10.1016/j.cpc.2005.07.008">To be or not to be Yutsis: algorithms for the decision problem</a>, Computer Physics Communications 173 (2005) 61-70.
%K nonn,more
%O 2,2
%A Dries Van Dyck (VanDyck.Dries(AT)Gmail.com), Mar 05 2006
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