Examples
The smallest hypohamiltonian graph is the Petersen graph (Herz, Duby & Vigué 1967). More generally, the generalized Petersen graph GP(n,2) is hypohamiltonian when n is 5 (mod 6); the Petersen graph is the instance of this construction with n = 5.
Lindgren (1967) found another infinite class of cubic graphs in which the number of vertices is 4 (mod 6). Lindgren's construction consists of a cycle of length 3 (mod 6) and a single central vertex; the central vertex is connected to every third vertex of the cycle by edges he calls spokes, and the vertices two positions away from each spoke endpoint are connected to each other. Again, the smallest instance of Lindgren's construction is the Petersen graph.
Additional infinite families are given by Bondy (1972), Doyen & van Diest (1975), and Gutt (1977).
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