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A328061
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Number of 4-chromatic Laman graphs on n vertices.
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1
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OFFSET
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7,2
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COMMENTS
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All the Laman graphs (in other terms, 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.
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LINKS
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Table of n, a(n) for n=7..12.
L. Henneberg, Die graphische Statik der starren Systeme, Leipzig, 1911.
Christoph Koutschan, Mathematica program for generating a list of non-isomorphic Laman graphs on n vertices.
G. Laman, On Graphs and Rigidity of Plane Skeletal Structures, J. Engineering Mathematics, Vol. 4, No. 4, 1970, pp. 331-340; alternative link.
A. Nixon, E. Ross, One brick at a time: a survey of inductive constructions in rigidity theory, arXiv:1203.6623 [math.MG], 2012-2013.
Vsevolod Voronov, Anna Neopryatnaya, and Eugene Dergachev, Constructing 5-chromatic unit distance graphs embedded in the Euclidean plane and two-dimensional spheres, arXiv:2106.11824 [math.CO], 2021.
Eric Weisstein's World of Mathematics, Moser spindle is a 4-chromatic Laman graph.
Wikipedia, Laman graph
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MATHEMATICA
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Table[Length[
Select[LamanGraphs[n],
IGChromaticNumber[AdjacencyGraph[G2Mat[#]]] == 4 &]], {n, 7, 9}]
(* using the program by Christoph Koutschan for generating Laman graphs, see A227117, and IGraph/M interface by Szabolcs Horvát *)
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CROSSREFS
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Cf. A227117, A273468, A328060.
Sequence in context: A307461 A318213 A001575 * A305603 A333985 A297069
Adjacent sequences: A328058 A328059 A328060 * A328062 A328063 A328064
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KEYWORD
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nonn,more
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AUTHOR
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Vsevolod Voronov, Oct 03 2019
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STATUS
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approved
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