%I A115340
%S A115340 1,1,2,5,14,50,233,1248,7593,49536,339483,2404472,17468202,129459090,
%T A115340 975647292,7458907217,57744122366,452028275567
%N A115340 Number of dual hamiltonian cubic polyhedra or planar 3-connected Yutsis 
               graphs on 2n nodes.
%C A115340 Yutsis graphs are connected cubic graphs which can be partitioned into 
               two vertex-induced trees, which are necessarily of the same size. 
               The cut seperating both trees contains n+2 edges for a graph on 2n 
               nodes, forming a hamiltonian cycle in the planar dual if the graph 
               is planar. These graphs are maximal in the number of nodes of the 
               largest vertex-induced forests among the connected cubic graphs (floor((6n-2)/
               4) for a graph on 2n nodes). Whitney showed in 1931 that proving 
               the 4-color theorem for a planar Yutsis graph implies the theorem 
               for all planar graphs.
%D A115340 F. Jaeger, On vertex induced-forests in cubic graphs, Proceedings 5th 
               Southeastern Conference, Congressus Numerantium (1974) 501-512
%D A115340 L. H. Kauffman, Map Coloring and the Vector Cross Product, Journal of 
               Combinatorial Theory, Series B, 48 (1990) 145-154
%D A115340 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
%H A115340 Dries Van Dyck, Veerle Fack, <a href="http://caagt.ugent.be/yutsis/">
               Yutsis project</a>
%Y A115340 Sequence in context: A006390 A100597 A022562 this_sequence A000109 A049338 
               A115275
%Y A115340 Adjacent sequences: A115337 A115338 A115339 this_sequence A115341 A115342 
               A115343
%K A115340 nice,nonn
%O A115340 2,3
%A A115340 Dries Van Dyck (VanDyck.Dries(AT)Gmail.com), Mar 06 2006