cp's OEIS Frontend

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.

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 first nontrivial bipartite Laman graph is K_{3,3}. An infinite sequence of such graphs can be obtained from K_{3,3} by Henneberg moves of the first type (i.e., adding a vertex and connecting it with two of the existing vertices from the one part).