Search: id:A115340 Results 1-1 of 1 results found. %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, Yutsis project %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 Search completed in 0.001 seconds