The Lindgren-Sousselier graphs are a sequence of hypohamiltonian graphs on vertices independently discovered by Sousselier (Herz et
al. 1967) and Lindgren (1967). However, according to correspondence between V. Chvátal
and D. E. Knuth in the mid-2020's, Berge (1970, p. 214) contains a
footnote which mentions that Sousselier wrote Berge on Jan. 6, 1963 stating,
"this [result] stems from a property that I discovered 31 years ago and never
published." It therefore appears that Sousslier constructed (but did not publish)
the Lindgren-Sousselier graphs as early as 1932 (D. E. Knuth, pers. comm.,
Feb. 6, 2026).
The first Lindgren-Sousselier graphs are illustrated above for , 2, ..., where, in this indexing convention, the graph with
is the Petersen graph.
A number of different embeddings of the Lindgren-Sousselier graph on 28 vertices are illustrated above.
The Lindgren-Sousselier graph indexed by has graph crossing number
and rectilinear crossing number
and local crossing number 1. The Lindgren-Sousselier
graphs are therefore nonplanar 1-planar
graphs.
The Lindgren-Sousselier graphs are platypus graphs.