| Barnette–Bosák–Lederberg graph | |
| Vertices: | 38 |
| Edges: | 57 |
| Girth: | 4 |
| Radius: | 5 |
| Diameter: | 9 |
| Chromatic Number: | 3 |
| Chromatic Index: | 3 |
| Properties: | Cubic Planar Polyhedral |
In the mathematical field of graph theory, the Barnette–Bosák–Lederberg graph is a cubic (that is, 3-regular) polyhedral graph with no Hamiltonian cycle, the smallest such graph possible. It was discovered in the mid-1960s by Joshua Lederberg, David Barnette, and Juraj Bosák, after whom it is named. It has 38 vertices and 57 edges.
Other larger non-Hamiltonian cubic polyhedral graphs include the 46-vertex Tutte graph and a 44-vertex graph found by Emanuels Grīnbergs using Grinberg's theorem.The Barnette–Bosák–Lederberg graph has a similar construction to the Tutte graph but is composed of two Tutte fragments, connected through a pentagonal prism, instead of three connected through a tetrahedron.Without the constraint of having exactly three edges at every vertex, much smaller non-Hamiltonian polyhedral graphs are possible, including the Goldner–Harary graph and the Herschel graph.