This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A328061 #46 Jun 02 2025 17:24:04
%S A328061 1,8,102,1601,29811,636686,15298955,407748141,11932078866
%N A328061 Number of 4-chromatic Laman graphs on n vertices.
%C A328061 All the Laman graphs (in other words, minimally rigid graphs) can be constructed by the inductive Henneberg construction, i.e., a sequence of Henneberg steps starting from K_2. A new vertex added by a Henneberg move is connected with two or three of the previously existing vertices. Hence, the chromatic number of a Laman graph can be 2, 3 or 4. One can hypothesize that the set of 3-chromatic Laman graphs is the largest and that bipartite graphs are relatively rare. The simplest example of a 4-chromatic Laman graph is the Moser spindle.
%H A328061 L. Henneberg, <a href="https://archive.org/details/diegraphischest00henngoog">Die graphische Statik der starren Systeme</a>, Leipzig, 1911.
%H A328061 Christoph Koutschan, <a href="https://oeis.org/A227117/a227117_2.txt">Mathematica program</a> for generating a list of non-isomorphic Laman graphs on n vertices.
%H A328061 G. Laman, <a href="https://doi.org/10.1007/BF01534980">On Graphs and Rigidity of Plane Skeletal Structures</a>, J. Engineering Mathematics, Vol. 4, No. 4, 1970, pp. 331-340; <a href="https://platformwiskunde.nl/wp-content/uploads/2021/02/ref_jenma.pdf">alternative link</a>.
%H A328061 Martin Larsson, <a href="https://github.com/martinkjlarsson/nauty-laman-plugin">Nauty Laman plugin</a>
%H A328061 A. Nixon, E. Ross, <a href="https://arxiv.org/abs/1203.6623">One brick at a time: a survey of inductive constructions in rigidity theory</a>, arXiv:1203.6623 [math.MG], 2012-2013.
%H A328061 Vsevolod Voronov, Anna Neopryatnaya, and Eugene Dergachev, <a href="https://arxiv.org/abs/2106.11824">Constructing 5-chromatic unit distance graphs embedded in the Euclidean plane and two-dimensional spheres</a>, arXiv:2106.11824 [math.CO], 2021.
%H A328061 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MoserSpindle.html">Moser spindle</a> is a 4-chromatic Laman graph.
%H A328061 Wikipedia, <a href="https://en.wikipedia.org/wiki/Laman_graph">Laman graph</a>
%t A328061 Table[Length[
%t A328061 Select[LamanGraphs[n],
%t A328061 IGChromaticNumber[AdjacencyGraph[G2Mat[#]]] == 4 &]], {n, 7, 9}]
%t A328061 (* using the program by Christoph Koutschan for generating Laman graphs, see A227117, and IGraph/M interface by Szabolcs Horvát *)
%o A328061 (nauty) gensparseg $n -K2 | countg --N # With Laman plugin; see link.
%Y A328061 Cf. A227117, A273468, A328060.
%K A328061 nonn,more
%O A328061 7,2
%A A328061 _Vsevolod Voronov_, Oct 03 2019
%E A328061 a(13)-a(15) added by _Georg Grasegger_, Sep 09 2024