The Moser spindle, a planar Laman graph drawn as a pointed pseudotriangulationThe complete bipartite graph K3,3, a non-planar Laman graph
In graph theory, the Laman graphs are a family of sparse graphs describing the minimally rigid systems of rods and joints in the plane. Formally, a Laman graph is a graph on n vertices such that, for all k, every k-vertex subgraph has at most 2k − 3 edges, and such that the whole graph has exactly 2n − 3 edges. Laman graphs are named after Gerard Laman, of the University of Amsterdam, who in 1970 used them to characterize rigid planar structures.[1]
This characterization, however, had already been discovered in 1927 by Hilda Geiringer.[2]
^Laman, G. (1970), "On graphs and the rigidity of plane skeletal structures", J. Engineering Mathematics, 4 (4): 331–340, Bibcode:1970JEnMa...4..331L, doi:10.1007/BF01534980, MR 0269535, S2CID 122631794.
^Pollaczek‐Geiringer, Hilda (1927), "Über die Gliederung ebener Fachwerke", Zeitschrift für Angewandte Mathematik und Mechanik, 7 (1): 58–72, Bibcode:1927ZaMM....7...58P, doi:10.1002/zamm.19270070107.
In graph theory, the Lamangraphs are a family of sparse graphs describing the minimally rigid systems of rods and joints in the plane. Formally, a Laman...
two-dimensional rigidity matroid (the minimally rigid graphs in the plane) are the Lamangraphs. Cauchy's theorem states that a three-dimensional convex...
matchstick graph. The Moser spindle is also a Lamangraph, meaning that it forms a minimally rigid system when embedded in the plane. As a planar Lamangraph, it...
exactly the (1,0)-sparse graphs, and the Lamangraphs arising in rigidity theory are exactly the (2,3)-tight graphs. Other graph families not characterized...
Gerard Laman (August 22, 1924 – September 22, 2009) was a Dutch mathematician who worked on graph theory. He completed high school studies at the Stedelijk...
well-covered graphs, the study of graph crossing numbers, and the theory of graph minors. The utility graph K 3 , 3 {\displaystyle K_{3,3}} is a Lamangraph, meaning...
graphs in two dimensions. Every planar Lamangraph can be drawn as a pointed pseudotriangulation, although not every planar drawing of a planar Laman...
from a group, each give rise to a biased graph and therefore have frame and lift matroids. The Lamangraphs form the bases of the two dimensional rigidity...
dn minus the matroid rank. In two-dimensional rigidity matroids, the Lamangraphs play the role that spanning trees play in graphic matroids, but the structure...
frameworks in two dimensions) have come to be known as Lamangraphs. The family of Lamangraphs on a fixed set of n {\displaystyle n} vertices forms the...
characterizes the planar Lamangraphs, the minimally rigid graphs that can be embedded without crossings in the plane, as the graphs of pseudotriangulations...
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..7...58P. doi:10.1002/zamm.19270070107. ISSN 1521-4001. Laman, G. (1970-10-01). "On graphs and rigidity of plane skeletal structures". Journal of Engineering...
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