A111358 Numbers of planar triangulations with minimum degree 5 and without separating 3- or 4-cycles - that is 3- or 4-cycles where the interior and exterior contain at least one vertex.

1, 0, 1, 1, 3, 4, 12, 23, 71, 187, 627, 1970, 6833, 23384, 82625, 292164, 1045329, 3750277, 13532724, 48977625, 177919099, 648145255, 2368046117, 8674199554, 31854078139, 117252592450, 432576302286, 1599320144703, 5925181102878

Offset: 12

Author

Gunnar Brinkmann, Nov 07 2005

Keywords

• nonn

Comments

A006791 and this sequence are the same sequence. The correspondence is just that these objects are planar duals of each other. But the offset and step are different: if the cubic graph has 2*n vertices, the dual triangulation has n+2 vertices. - Brendan McKay, May 24 2017

Also the number of 5-connected triangulations on n vertices. - Manfred Scheucher, Mar 17 2023

Examples

			The icosahedron is the smallest triangulation with minimum degree 5 and it doesn't contain any separating 3- or 4-cycles. Examples can easily be seen as 2D and 3D pictures using the program CaGe cited above.
		

Links

• G. Brinkmann, CaGe.
• Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
• Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph. [Cached copy, pdf file only, no active links, with permission]
• G. Brinkmann and Brendan D. McKay, Construction of planar triangulations with minimum degree 5 , Disc. Math. vol 301, iss. 2-3 (2005) 147-163.
• D. A. Holton and B. D. McKay, The smallest non-hamiltonian 3-connected cubic planar graphs have 38 vertices, J. Combinat. Theory B vol 45, iss. 3 (1988) 305-319.
• D. A. Holton and B. D. McKay, Erratum, J. Combinat. Theory B vol 47, iss. 2 (1989) 248.

Crossrefs

Cf. A081621, A007894, A006791, A000109, A007021, A361578.